Integral de 20*x^2/(((x^2*x-3)*(x+1))) dx
Solución
Solución detallada
Hay varias maneras de calcular esta integral.
Método #1
Vuelva a escribir el integrando:
20 x 2 ( x + 1 ) ( x x 2 − 3 ) = 5 ( x 2 + 3 x − 3 ) x 3 − 3 − 5 x + 1 \frac{20 x^{2}}{\left(x + 1\right) \left(x x^{2} - 3\right)} = \frac{5 \left(x^{2} + 3 x - 3\right)}{x^{3} - 3} - \frac{5}{x + 1} ( x + 1 ) ( x x 2 − 3 ) 20 x 2 = x 3 − 3 5 ( x 2 + 3 x − 3 ) − x + 1 5
Integramos término a término:
La integral del producto de una función por una constante es la constante por la integral de esta función:
∫ 5 ( x 2 + 3 x − 3 ) x 3 − 3 d x = 5 ∫ x 2 + 3 x − 3 x 3 − 3 d x \int \frac{5 \left(x^{2} + 3 x - 3\right)}{x^{3} - 3}\, dx = 5 \int \frac{x^{2} + 3 x - 3}{x^{3} - 3}\, dx ∫ x 3 − 3 5 ( x 2 + 3 x − 3 ) d x = 5 ∫ x 3 − 3 x 2 + 3 x − 3 d x
Vuelva a escribir el integrando:
x 2 + 3 x − 3 x 3 − 3 = x 2 x 3 − 3 + 3 x x 3 − 3 − 3 x 3 − 3 \frac{x^{2} + 3 x - 3}{x^{3} - 3} = \frac{x^{2}}{x^{3} - 3} + \frac{3 x}{x^{3} - 3} - \frac{3}{x^{3} - 3} x 3 − 3 x 2 + 3 x − 3 = x 3 − 3 x 2 + x 3 − 3 3 x − x 3 − 3 3
Integramos término a término:
que u = x 3 − 3 u = x^{3} - 3 u = x 3 − 3 .
Luego que d u = 3 x 2 d x du = 3 x^{2} dx d u = 3 x 2 d x y ponemos d u 3 \frac{du}{3} 3 d u :
∫ 1 3 u d u \int \frac{1}{3 u}\, du ∫ 3 u 1 d u
La integral del producto de una función por una constante es la constante por la integral de esta función:
∫ 1 u d u = ∫ 1 u d u 3 \int \frac{1}{u}\, du = \frac{\int \frac{1}{u}\, du}{3} ∫ u 1 d u = 3 ∫ u 1 d u
Integral 1 u \frac{1}{u} u 1 es log ( u ) \log{\left(u \right)} log ( u ) .
Por lo tanto, el resultado es: log ( u ) 3 \frac{\log{\left(u \right)}}{3} 3 l o g ( u )
Si ahora sustituir u u u más en:
log ( x 3 − 3 ) 3 \frac{\log{\left(x^{3} - 3 \right)}}{3} 3 l o g ( x 3 − 3 )
La integral del producto de una función por una constante es la constante por la integral de esta función:
∫ 3 x x 3 − 3 d x = 3 ∫ x x 3 − 3 d x \int \frac{3 x}{x^{3} - 3}\, dx = 3 \int \frac{x}{x^{3} - 3}\, dx ∫ x 3 − 3 3 x d x = 3 ∫ x 3 − 3 x d x
No puedo encontrar los pasos en la búsqueda de esta integral.
Pero la integral
3 2 3 log ( x − 3 3 ) 9 − 3 2 3 log ( x 2 + 3 3 x + 3 2 3 ) 18 + 3 6 atan ( 2 3 6 x 3 + 3 3 ) 3 \frac{3^{\frac{2}{3}} \log{\left(x - \sqrt[3]{3} \right)}}{9} - \frac{3^{\frac{2}{3}} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{18} + \frac{\sqrt[6]{3} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{3} 9 3 3 2 l o g ( x − 3 3 ) − 18 3 3 2 l o g ( x 2 + 3 3 x + 3 3 2 ) + 3 6 3 atan ( 3 2 6 3 x + 3 3 )
Por lo tanto, el resultado es: 3 2 3 log ( x − 3 3 ) 3 − 3 2 3 log ( x 2 + 3 3 x + 3 2 3 ) 6 + 3 6 atan ( 2 3 6 x 3 + 3 3 ) \frac{3^{\frac{2}{3}} \log{\left(x - \sqrt[3]{3} \right)}}{3} - \frac{3^{\frac{2}{3}} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \sqrt[6]{3} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)} 3 3 3 2 l o g ( x − 3 3 ) − 6 3 3 2 l o g ( x 2 + 3 3 x + 3 3 2 ) + 6 3 atan ( 3 2 6 3 x + 3 3 )
La integral del producto de una función por una constante es la constante por la integral de esta función:
∫ ( − 3 x 3 − 3 ) d x = − 3 ∫ 1 x 3 − 3 d x \int \left(- \frac{3}{x^{3} - 3}\right)\, dx = - 3 \int \frac{1}{x^{3} - 3}\, dx ∫ ( − x 3 − 3 3 ) d x = − 3 ∫ x 3 − 3 1 d x
No puedo encontrar los pasos en la búsqueda de esta integral.
Pero la integral
3 3 log ( x − 3 3 ) 9 − 3 3 log ( x 2 + 3 3 x + 3 2 3 ) 18 − 3 5 6 atan ( 2 3 6 x 3 + 3 3 ) 9 \frac{\sqrt[3]{3} \log{\left(x - \sqrt[3]{3} \right)}}{9} - \frac{\sqrt[3]{3} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{18} - \frac{3^{\frac{5}{6}} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{9} 9 3 3 l o g ( x − 3 3 ) − 18 3 3 l o g ( x 2 + 3 3 x + 3 3 2 ) − 9 3 6 5 atan ( 3 2 6 3 x + 3 3 )
Por lo tanto, el resultado es: − 3 3 log ( x − 3 3 ) 3 + 3 3 log ( x 2 + 3 3 x + 3 2 3 ) 6 + 3 5 6 atan ( 2 3 6 x 3 + 3 3 ) 3 - \frac{\sqrt[3]{3} \log{\left(x - \sqrt[3]{3} \right)}}{3} + \frac{\sqrt[3]{3} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \frac{3^{\frac{5}{6}} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{3} − 3 3 3 l o g ( x − 3 3 ) + 6 3 3 l o g ( x 2 + 3 3 x + 3 3 2 ) + 3 3 6 5 atan ( 3 2 6 3 x + 3 3 )
El resultado es: − 3 3 log ( x − 3 3 ) 3 + 3 2 3 log ( x − 3 3 ) 3 + log ( x 3 − 3 ) 3 − 3 2 3 log ( x 2 + 3 3 x + 3 2 3 ) 6 + 3 3 log ( x 2 + 3 3 x + 3 2 3 ) 6 + 3 5 6 atan ( 2 3 6 x 3 + 3 3 ) 3 + 3 6 atan ( 2 3 6 x 3 + 3 3 ) - \frac{\sqrt[3]{3} \log{\left(x - \sqrt[3]{3} \right)}}{3} + \frac{3^{\frac{2}{3}} \log{\left(x - \sqrt[3]{3} \right)}}{3} + \frac{\log{\left(x^{3} - 3 \right)}}{3} - \frac{3^{\frac{2}{3}} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \frac{\sqrt[3]{3} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \frac{3^{\frac{5}{6}} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{3} + \sqrt[6]{3} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)} − 3 3 3 l o g ( x − 3 3 ) + 3 3 3 2 l o g ( x − 3 3 ) + 3 l o g ( x 3 − 3 ) − 6 3 3 2 l o g ( x 2 + 3 3 x + 3 3 2 ) + 6 3 3 l o g ( x 2 + 3 3 x + 3 3 2 ) + 3 3 6 5 atan ( 3 2 6 3 x + 3 3 ) + 6 3 atan ( 3 2 6 3 x + 3 3 )
Por lo tanto, el resultado es: − 5 3 3 log ( x − 3 3 ) 3 + 5 ⋅ 3 2 3 log ( x − 3 3 ) 3 + 5 log ( x 3 − 3 ) 3 − 5 ⋅ 3 2 3 log ( x 2 + 3 3 x + 3 2 3 ) 6 + 5 3 3 log ( x 2 + 3 3 x + 3 2 3 ) 6 + 5 ⋅ 3 5 6 atan ( 2 3 6 x 3 + 3 3 ) 3 + 5 3 6 atan ( 2 3 6 x 3 + 3 3 ) - \frac{5 \sqrt[3]{3} \log{\left(x - \sqrt[3]{3} \right)}}{3} + \frac{5 \cdot 3^{\frac{2}{3}} \log{\left(x - \sqrt[3]{3} \right)}}{3} + \frac{5 \log{\left(x^{3} - 3 \right)}}{3} - \frac{5 \cdot 3^{\frac{2}{3}} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \frac{5 \sqrt[3]{3} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \frac{5 \cdot 3^{\frac{5}{6}} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{3} + 5 \sqrt[6]{3} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)} − 3 5 3 3 l o g ( x − 3 3 ) + 3 5 ⋅ 3 3 2 l o g ( x − 3 3 ) + 3 5 l o g ( x 3 − 3 ) − 6 5 ⋅ 3 3 2 l o g ( x 2 + 3 3 x + 3 3 2 ) + 6 5 3 3 l o g ( x 2 + 3 3 x + 3 3 2 ) + 3 5 ⋅ 3 6 5 atan ( 3 2 6 3 x + 3 3 ) + 5 6 3 atan ( 3 2 6 3 x + 3 3 )
La integral del producto de una función por una constante es la constante por la integral de esta función:
∫ ( − 5 x + 1 ) d x = − 5 ∫ 1 x + 1 d x \int \left(- \frac{5}{x + 1}\right)\, dx = - 5 \int \frac{1}{x + 1}\, dx ∫ ( − x + 1 5 ) d x = − 5 ∫ x + 1 1 d x
que u = x + 1 u = x + 1 u = x + 1 .
Luego que d u = d x du = dx d u = d x y ponemos d u du d u :
∫ 1 u d u \int \frac{1}{u}\, du ∫ u 1 d u
Integral 1 u \frac{1}{u} u 1 es log ( u ) \log{\left(u \right)} log ( u ) .
Si ahora sustituir u u u más en:
log ( x + 1 ) \log{\left(x + 1 \right)} log ( x + 1 )
Por lo tanto, el resultado es: − 5 log ( x + 1 ) - 5 \log{\left(x + 1 \right)} − 5 log ( x + 1 )
El resultado es: − 5 log ( x + 1 ) − 5 3 3 log ( x − 3 3 ) 3 + 5 ⋅ 3 2 3 log ( x − 3 3 ) 3 + 5 log ( x 3 − 3 ) 3 − 5 ⋅ 3 2 3 log ( x 2 + 3 3 x + 3 2 3 ) 6 + 5 3 3 log ( x 2 + 3 3 x + 3 2 3 ) 6 + 5 ⋅ 3 5 6 atan ( 2 3 6 x 3 + 3 3 ) 3 + 5 3 6 atan ( 2 3 6 x 3 + 3 3 ) - 5 \log{\left(x + 1 \right)} - \frac{5 \sqrt[3]{3} \log{\left(x - \sqrt[3]{3} \right)}}{3} + \frac{5 \cdot 3^{\frac{2}{3}} \log{\left(x - \sqrt[3]{3} \right)}}{3} + \frac{5 \log{\left(x^{3} - 3 \right)}}{3} - \frac{5 \cdot 3^{\frac{2}{3}} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \frac{5 \sqrt[3]{3} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \frac{5 \cdot 3^{\frac{5}{6}} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{3} + 5 \sqrt[6]{3} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)} − 5 log ( x + 1 ) − 3 5 3 3 l o g ( x − 3 3 ) + 3 5 ⋅ 3 3 2 l o g ( x − 3 3 ) + 3 5 l o g ( x 3 − 3 ) − 6 5 ⋅ 3 3 2 l o g ( x 2 + 3 3 x + 3 3 2 ) + 6 5 3 3 l o g ( x 2 + 3 3 x + 3 3 2 ) + 3 5 ⋅ 3 6 5 atan ( 3 2 6 3 x + 3 3 ) + 5 6 3 atan ( 3 2 6 3 x + 3 3 )
Método #2
Vuelva a escribir el integrando:
20 x 2 ( x + 1 ) ( x x 2 − 3 ) = 20 x 2 x 4 + x 3 − 3 x − 3 \frac{20 x^{2}}{\left(x + 1\right) \left(x x^{2} - 3\right)} = \frac{20 x^{2}}{x^{4} + x^{3} - 3 x - 3} ( x + 1 ) ( x x 2 − 3 ) 20 x 2 = x 4 + x 3 − 3 x − 3 20 x 2
La integral del producto de una función por una constante es la constante por la integral de esta función:
∫ 20 x 2 x 4 + x 3 − 3 x − 3 d x = 20 ∫ x 2 x 4 + x 3 − 3 x − 3 d x \int \frac{20 x^{2}}{x^{4} + x^{3} - 3 x - 3}\, dx = 20 \int \frac{x^{2}}{x^{4} + x^{3} - 3 x - 3}\, dx ∫ x 4 + x 3 − 3 x − 3 20 x 2 d x = 20 ∫ x 4 + x 3 − 3 x − 3 x 2 d x
Vuelva a escribir el integrando:
x 2 x 4 + x 3 − 3 x − 3 = x 2 + 3 x − 3 4 ( x 3 − 3 ) − 1 4 ( x + 1 ) \frac{x^{2}}{x^{4} + x^{3} - 3 x - 3} = \frac{x^{2} + 3 x - 3}{4 \left(x^{3} - 3\right)} - \frac{1}{4 \left(x + 1\right)} x 4 + x 3 − 3 x − 3 x 2 = 4 ( x 3 − 3 ) x 2 + 3 x − 3 − 4 ( x + 1 ) 1
Integramos término a término:
La integral del producto de una función por una constante es la constante por la integral de esta función:
∫ x 2 + 3 x − 3 4 ( x 3 − 3 ) d x = ∫ x 2 + 3 x − 3 x 3 − 3 d x 4 \int \frac{x^{2} + 3 x - 3}{4 \left(x^{3} - 3\right)}\, dx = \frac{\int \frac{x^{2} + 3 x - 3}{x^{3} - 3}\, dx}{4} ∫ 4 ( x 3 − 3 ) x 2 + 3 x − 3 d x = 4 ∫ x 3 − 3 x 2 + 3 x − 3 d x
Vuelva a escribir el integrando:
x 2 + 3 x − 3 x 3 − 3 = x 2 x 3 − 3 + 3 x x 3 − 3 − 3 x 3 − 3 \frac{x^{2} + 3 x - 3}{x^{3} - 3} = \frac{x^{2}}{x^{3} - 3} + \frac{3 x}{x^{3} - 3} - \frac{3}{x^{3} - 3} x 3 − 3 x 2 + 3 x − 3 = x 3 − 3 x 2 + x 3 − 3 3 x − x 3 − 3 3
Integramos término a término:
que u = x 3 − 3 u = x^{3} - 3 u = x 3 − 3 .
Luego que d u = 3 x 2 d x du = 3 x^{2} dx d u = 3 x 2 d x y ponemos d u 3 \frac{du}{3} 3 d u :
∫ 1 3 u d u \int \frac{1}{3 u}\, du ∫ 3 u 1 d u
La integral del producto de una función por una constante es la constante por la integral de esta función:
∫ 1 u d u = ∫ 1 u d u 3 \int \frac{1}{u}\, du = \frac{\int \frac{1}{u}\, du}{3} ∫ u 1 d u = 3 ∫ u 1 d u
Integral 1 u \frac{1}{u} u 1 es log ( u ) \log{\left(u \right)} log ( u ) .
Por lo tanto, el resultado es: log ( u ) 3 \frac{\log{\left(u \right)}}{3} 3 l o g ( u )
Si ahora sustituir u u u más en:
log ( x 3 − 3 ) 3 \frac{\log{\left(x^{3} - 3 \right)}}{3} 3 l o g ( x 3 − 3 )
La integral del producto de una función por una constante es la constante por la integral de esta función:
∫ 3 x x 3 − 3 d x = 3 ∫ x x 3 − 3 d x \int \frac{3 x}{x^{3} - 3}\, dx = 3 \int \frac{x}{x^{3} - 3}\, dx ∫ x 3 − 3 3 x d x = 3 ∫ x 3 − 3 x d x
No puedo encontrar los pasos en la búsqueda de esta integral.
Pero la integral
3 2 3 log ( x − 3 3 ) 9 − 3 2 3 log ( x 2 + 3 3 x + 3 2 3 ) 18 + 3 6 atan ( 2 3 6 x 3 + 3 3 ) 3 \frac{3^{\frac{2}{3}} \log{\left(x - \sqrt[3]{3} \right)}}{9} - \frac{3^{\frac{2}{3}} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{18} + \frac{\sqrt[6]{3} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{3} 9 3 3 2 l o g ( x − 3 3 ) − 18 3 3 2 l o g ( x 2 + 3 3 x + 3 3 2 ) + 3 6 3 atan ( 3 2 6 3 x + 3 3 )
Por lo tanto, el resultado es: 3 2 3 log ( x − 3 3 ) 3 − 3 2 3 log ( x 2 + 3 3 x + 3 2 3 ) 6 + 3 6 atan ( 2 3 6 x 3 + 3 3 ) \frac{3^{\frac{2}{3}} \log{\left(x - \sqrt[3]{3} \right)}}{3} - \frac{3^{\frac{2}{3}} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \sqrt[6]{3} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)} 3 3 3 2 l o g ( x − 3 3 ) − 6 3 3 2 l o g ( x 2 + 3 3 x + 3 3 2 ) + 6 3 atan ( 3 2 6 3 x + 3 3 )
La integral del producto de una función por una constante es la constante por la integral de esta función:
∫ ( − 3 x 3 − 3 ) d x = − 3 ∫ 1 x 3 − 3 d x \int \left(- \frac{3}{x^{3} - 3}\right)\, dx = - 3 \int \frac{1}{x^{3} - 3}\, dx ∫ ( − x 3 − 3 3 ) d x = − 3 ∫ x 3 − 3 1 d x
No puedo encontrar los pasos en la búsqueda de esta integral.
Pero la integral
3 3 log ( x − 3 3 ) 9 − 3 3 log ( x 2 + 3 3 x + 3 2 3 ) 18 − 3 5 6 atan ( 2 3 6 x 3 + 3 3 ) 9 \frac{\sqrt[3]{3} \log{\left(x - \sqrt[3]{3} \right)}}{9} - \frac{\sqrt[3]{3} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{18} - \frac{3^{\frac{5}{6}} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{9} 9 3 3 l o g ( x − 3 3 ) − 18 3 3 l o g ( x 2 + 3 3 x + 3 3 2 ) − 9 3 6 5 atan ( 3 2 6 3 x + 3 3 )
Por lo tanto, el resultado es: − 3 3 log ( x − 3 3 ) 3 + 3 3 log ( x 2 + 3 3 x + 3 2 3 ) 6 + 3 5 6 atan ( 2 3 6 x 3 + 3 3 ) 3 - \frac{\sqrt[3]{3} \log{\left(x - \sqrt[3]{3} \right)}}{3} + \frac{\sqrt[3]{3} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \frac{3^{\frac{5}{6}} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{3} − 3 3 3 l o g ( x − 3 3 ) + 6 3 3 l o g ( x 2 + 3 3 x + 3 3 2 ) + 3 3 6 5 atan ( 3 2 6 3 x + 3 3 )
El resultado es: − 3 3 log ( x − 3 3 ) 3 + 3 2 3 log ( x − 3 3 ) 3 + log ( x 3 − 3 ) 3 − 3 2 3 log ( x 2 + 3 3 x + 3 2 3 ) 6 + 3 3 log ( x 2 + 3 3 x + 3 2 3 ) 6 + 3 5 6 atan ( 2 3 6 x 3 + 3 3 ) 3 + 3 6 atan ( 2 3 6 x 3 + 3 3 ) - \frac{\sqrt[3]{3} \log{\left(x - \sqrt[3]{3} \right)}}{3} + \frac{3^{\frac{2}{3}} \log{\left(x - \sqrt[3]{3} \right)}}{3} + \frac{\log{\left(x^{3} - 3 \right)}}{3} - \frac{3^{\frac{2}{3}} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \frac{\sqrt[3]{3} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \frac{3^{\frac{5}{6}} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{3} + \sqrt[6]{3} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)} − 3 3 3 l o g ( x − 3 3 ) + 3 3 3 2 l o g ( x − 3 3 ) + 3 l o g ( x 3 − 3 ) − 6 3 3 2 l o g ( x 2 + 3 3 x + 3 3 2 ) + 6 3 3 l o g ( x 2 + 3 3 x + 3 3 2 ) + 3 3 6 5 atan ( 3 2 6 3 x + 3 3 ) + 6 3 atan ( 3 2 6 3 x + 3 3 )
Por lo tanto, el resultado es: − 3 3 log ( x − 3 3 ) 12 + 3 2 3 log ( x − 3 3 ) 12 + log ( x 3 − 3 ) 12 − 3 2 3 log ( x 2 + 3 3 x + 3 2 3 ) 24 + 3 3 log ( x 2 + 3 3 x + 3 2 3 ) 24 + 3 5 6 atan ( 2 3 6 x 3 + 3 3 ) 12 + 3 6 atan ( 2 3 6 x 3 + 3 3 ) 4 - \frac{\sqrt[3]{3} \log{\left(x - \sqrt[3]{3} \right)}}{12} + \frac{3^{\frac{2}{3}} \log{\left(x - \sqrt[3]{3} \right)}}{12} + \frac{\log{\left(x^{3} - 3 \right)}}{12} - \frac{3^{\frac{2}{3}} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{24} + \frac{\sqrt[3]{3} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{24} + \frac{3^{\frac{5}{6}} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{12} + \frac{\sqrt[6]{3} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{4} − 12 3 3 l o g ( x − 3 3 ) + 12 3 3 2 l o g ( x − 3 3 ) + 12 l o g ( x 3 − 3 ) − 24 3 3 2 l o g ( x 2 + 3 3 x + 3 3 2 ) + 24 3 3 l o g ( x 2 + 3 3 x + 3 3 2 ) + 12 3 6 5 atan ( 3 2 6 3 x + 3 3 ) + 4 6 3 atan ( 3 2 6 3 x + 3 3 )
La integral del producto de una función por una constante es la constante por la integral de esta función:
∫ ( − 1 4 ( x + 1 ) ) d x = − ∫ 1 x + 1 d x 4 \int \left(- \frac{1}{4 \left(x + 1\right)}\right)\, dx = - \frac{\int \frac{1}{x + 1}\, dx}{4} ∫ ( − 4 ( x + 1 ) 1 ) d x = − 4 ∫ x + 1 1 d x
que u = x + 1 u = x + 1 u = x + 1 .
Luego que d u = d x du = dx d u = d x y ponemos d u du d u :
∫ 1 u d u \int \frac{1}{u}\, du ∫ u 1 d u
Integral 1 u \frac{1}{u} u 1 es log ( u ) \log{\left(u \right)} log ( u ) .
Si ahora sustituir u u u más en:
log ( x + 1 ) \log{\left(x + 1 \right)} log ( x + 1 )
Por lo tanto, el resultado es: − log ( x + 1 ) 4 - \frac{\log{\left(x + 1 \right)}}{4} − 4 l o g ( x + 1 )
El resultado es: − log ( x + 1 ) 4 − 3 3 log ( x − 3 3 ) 12 + 3 2 3 log ( x − 3 3 ) 12 + log ( x 3 − 3 ) 12 − 3 2 3 log ( x 2 + 3 3 x + 3 2 3 ) 24 + 3 3 log ( x 2 + 3 3 x + 3 2 3 ) 24 + 3 5 6 atan ( 2 3 6 x 3 + 3 3 ) 12 + 3 6 atan ( 2 3 6 x 3 + 3 3 ) 4 - \frac{\log{\left(x + 1 \right)}}{4} - \frac{\sqrt[3]{3} \log{\left(x - \sqrt[3]{3} \right)}}{12} + \frac{3^{\frac{2}{3}} \log{\left(x - \sqrt[3]{3} \right)}}{12} + \frac{\log{\left(x^{3} - 3 \right)}}{12} - \frac{3^{\frac{2}{3}} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{24} + \frac{\sqrt[3]{3} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{24} + \frac{3^{\frac{5}{6}} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{12} + \frac{\sqrt[6]{3} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{4} − 4 l o g ( x + 1 ) − 12 3 3 l o g ( x − 3 3 ) + 12 3 3 2 l o g ( x − 3 3 ) + 12 l o g ( x 3 − 3 ) − 24 3 3 2 l o g ( x 2 + 3 3 x + 3 3 2 ) + 24 3 3 l o g ( x 2 + 3 3 x + 3 3 2 ) + 12 3 6 5 atan ( 3 2 6 3 x + 3 3 ) + 4 6 3 atan ( 3 2 6 3 x + 3 3 )
Por lo tanto, el resultado es: − 5 log ( x + 1 ) − 5 3 3 log ( x − 3 3 ) 3 + 5 ⋅ 3 2 3 log ( x − 3 3 ) 3 + 5 log ( x 3 − 3 ) 3 − 5 ⋅ 3 2 3 log ( x 2 + 3 3 x + 3 2 3 ) 6 + 5 3 3 log ( x 2 + 3 3 x + 3 2 3 ) 6 + 5 ⋅ 3 5 6 atan ( 2 3 6 x 3 + 3 3 ) 3 + 5 3 6 atan ( 2 3 6 x 3 + 3 3 ) - 5 \log{\left(x + 1 \right)} - \frac{5 \sqrt[3]{3} \log{\left(x - \sqrt[3]{3} \right)}}{3} + \frac{5 \cdot 3^{\frac{2}{3}} \log{\left(x - \sqrt[3]{3} \right)}}{3} + \frac{5 \log{\left(x^{3} - 3 \right)}}{3} - \frac{5 \cdot 3^{\frac{2}{3}} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \frac{5 \sqrt[3]{3} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \frac{5 \cdot 3^{\frac{5}{6}} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{3} + 5 \sqrt[6]{3} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)} − 5 log ( x + 1 ) − 3 5 3 3 l o g ( x − 3 3 ) + 3 5 ⋅ 3 3 2 l o g ( x − 3 3 ) + 3 5 l o g ( x 3 − 3 ) − 6 5 ⋅ 3 3 2 l o g ( x 2 + 3 3 x + 3 3 2 ) + 6 5 3 3 l o g ( x 2 + 3 3 x + 3 3 2 ) + 3 5 ⋅ 3 6 5 atan ( 3 2 6 3 x + 3 3 ) + 5 6 3 atan ( 3 2 6 3 x + 3 3 )
Método #3
Vuelva a escribir el integrando:
20 x 2 ( x + 1 ) ( x x 2 − 3 ) = 20 x 2 x 4 − 3 x + x x 2 − 3 \frac{20 x^{2}}{\left(x + 1\right) \left(x x^{2} - 3\right)} = \frac{20 x^{2}}{x^{4} - 3 x + x x^{2} - 3} ( x + 1 ) ( x x 2 − 3 ) 20 x 2 = x 4 − 3 x + x x 2 − 3 20 x 2
La integral del producto de una función por una constante es la constante por la integral de esta función:
∫ 20 x 2 x 4 − 3 x + x x 2 − 3 d x = 20 ∫ x 2 x 4 − 3 x + x x 2 − 3 d x \int \frac{20 x^{2}}{x^{4} - 3 x + x x^{2} - 3}\, dx = 20 \int \frac{x^{2}}{x^{4} - 3 x + x x^{2} - 3}\, dx ∫ x 4 − 3 x + x x 2 − 3 20 x 2 d x = 20 ∫ x 4 − 3 x + x x 2 − 3 x 2 d x
Vuelva a escribir el integrando:
x 2 x 4 − 3 x + x x 2 − 3 = x 2 + 3 x − 3 4 ( x 3 − 3 ) − 1 4 ( x + 1 ) \frac{x^{2}}{x^{4} - 3 x + x x^{2} - 3} = \frac{x^{2} + 3 x - 3}{4 \left(x^{3} - 3\right)} - \frac{1}{4 \left(x + 1\right)} x 4 − 3 x + x x 2 − 3 x 2 = 4 ( x 3 − 3 ) x 2 + 3 x − 3 − 4 ( x + 1 ) 1
Integramos término a término:
La integral del producto de una función por una constante es la constante por la integral de esta función:
∫ x 2 + 3 x − 3 4 ( x 3 − 3 ) d x = ∫ x 2 + 3 x − 3 x 3 − 3 d x 4 \int \frac{x^{2} + 3 x - 3}{4 \left(x^{3} - 3\right)}\, dx = \frac{\int \frac{x^{2} + 3 x - 3}{x^{3} - 3}\, dx}{4} ∫ 4 ( x 3 − 3 ) x 2 + 3 x − 3 d x = 4 ∫ x 3 − 3 x 2 + 3 x − 3 d x
Vuelva a escribir el integrando:
x 2 + 3 x − 3 x 3 − 3 = x 2 x 3 − 3 + 3 x x 3 − 3 − 3 x 3 − 3 \frac{x^{2} + 3 x - 3}{x^{3} - 3} = \frac{x^{2}}{x^{3} - 3} + \frac{3 x}{x^{3} - 3} - \frac{3}{x^{3} - 3} x 3 − 3 x 2 + 3 x − 3 = x 3 − 3 x 2 + x 3 − 3 3 x − x 3 − 3 3
Integramos término a término:
que u = x 3 − 3 u = x^{3} - 3 u = x 3 − 3 .
Luego que d u = 3 x 2 d x du = 3 x^{2} dx d u = 3 x 2 d x y ponemos d u 3 \frac{du}{3} 3 d u :
∫ 1 3 u d u \int \frac{1}{3 u}\, du ∫ 3 u 1 d u
La integral del producto de una función por una constante es la constante por la integral de esta función:
∫ 1 u d u = ∫ 1 u d u 3 \int \frac{1}{u}\, du = \frac{\int \frac{1}{u}\, du}{3} ∫ u 1 d u = 3 ∫ u 1 d u
Integral 1 u \frac{1}{u} u 1 es log ( u ) \log{\left(u \right)} log ( u ) .
Por lo tanto, el resultado es: log ( u ) 3 \frac{\log{\left(u \right)}}{3} 3 l o g ( u )
Si ahora sustituir u u u más en:
log ( x 3 − 3 ) 3 \frac{\log{\left(x^{3} - 3 \right)}}{3} 3 l o g ( x 3 − 3 )
La integral del producto de una función por una constante es la constante por la integral de esta función:
∫ 3 x x 3 − 3 d x = 3 ∫ x x 3 − 3 d x \int \frac{3 x}{x^{3} - 3}\, dx = 3 \int \frac{x}{x^{3} - 3}\, dx ∫ x 3 − 3 3 x d x = 3 ∫ x 3 − 3 x d x
No puedo encontrar los pasos en la búsqueda de esta integral.
Pero la integral
3 2 3 log ( x − 3 3 ) 9 − 3 2 3 log ( x 2 + 3 3 x + 3 2 3 ) 18 + 3 6 atan ( 2 3 6 x 3 + 3 3 ) 3 \frac{3^{\frac{2}{3}} \log{\left(x - \sqrt[3]{3} \right)}}{9} - \frac{3^{\frac{2}{3}} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{18} + \frac{\sqrt[6]{3} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{3} 9 3 3 2 l o g ( x − 3 3 ) − 18 3 3 2 l o g ( x 2 + 3 3 x + 3 3 2 ) + 3 6 3 atan ( 3 2 6 3 x + 3 3 )
Por lo tanto, el resultado es: 3 2 3 log ( x − 3 3 ) 3 − 3 2 3 log ( x 2 + 3 3 x + 3 2 3 ) 6 + 3 6 atan ( 2 3 6 x 3 + 3 3 ) \frac{3^{\frac{2}{3}} \log{\left(x - \sqrt[3]{3} \right)}}{3} - \frac{3^{\frac{2}{3}} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \sqrt[6]{3} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)} 3 3 3 2 l o g ( x − 3 3 ) − 6 3 3 2 l o g ( x 2 + 3 3 x + 3 3 2 ) + 6 3 atan ( 3 2 6 3 x + 3 3 )
La integral del producto de una función por una constante es la constante por la integral de esta función:
∫ ( − 3 x 3 − 3 ) d x = − 3 ∫ 1 x 3 − 3 d x \int \left(- \frac{3}{x^{3} - 3}\right)\, dx = - 3 \int \frac{1}{x^{3} - 3}\, dx ∫ ( − x 3 − 3 3 ) d x = − 3 ∫ x 3 − 3 1 d x
No puedo encontrar los pasos en la búsqueda de esta integral.
Pero la integral
3 3 log ( x − 3 3 ) 9 − 3 3 log ( x 2 + 3 3 x + 3 2 3 ) 18 − 3 5 6 atan ( 2 3 6 x 3 + 3 3 ) 9 \frac{\sqrt[3]{3} \log{\left(x - \sqrt[3]{3} \right)}}{9} - \frac{\sqrt[3]{3} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{18} - \frac{3^{\frac{5}{6}} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{9} 9 3 3 l o g ( x − 3 3 ) − 18 3 3 l o g ( x 2 + 3 3 x + 3 3 2 ) − 9 3 6 5 atan ( 3 2 6 3 x + 3 3 )
Por lo tanto, el resultado es: − 3 3 log ( x − 3 3 ) 3 + 3 3 log ( x 2 + 3 3 x + 3 2 3 ) 6 + 3 5 6 atan ( 2 3 6 x 3 + 3 3 ) 3 - \frac{\sqrt[3]{3} \log{\left(x - \sqrt[3]{3} \right)}}{3} + \frac{\sqrt[3]{3} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \frac{3^{\frac{5}{6}} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{3} − 3 3 3 l o g ( x − 3 3 ) + 6 3 3 l o g ( x 2 + 3 3 x + 3 3 2 ) + 3 3 6 5 atan ( 3 2 6 3 x + 3 3 )
El resultado es: − 3 3 log ( x − 3 3 ) 3 + 3 2 3 log ( x − 3 3 ) 3 + log ( x 3 − 3 ) 3 − 3 2 3 log ( x 2 + 3 3 x + 3 2 3 ) 6 + 3 3 log ( x 2 + 3 3 x + 3 2 3 ) 6 + 3 5 6 atan ( 2 3 6 x 3 + 3 3 ) 3 + 3 6 atan ( 2 3 6 x 3 + 3 3 ) - \frac{\sqrt[3]{3} \log{\left(x - \sqrt[3]{3} \right)}}{3} + \frac{3^{\frac{2}{3}} \log{\left(x - \sqrt[3]{3} \right)}}{3} + \frac{\log{\left(x^{3} - 3 \right)}}{3} - \frac{3^{\frac{2}{3}} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \frac{\sqrt[3]{3} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \frac{3^{\frac{5}{6}} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{3} + \sqrt[6]{3} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)} − 3 3 3 l o g ( x − 3 3 ) + 3 3 3 2 l o g ( x − 3 3 ) + 3 l o g ( x 3 − 3 ) − 6 3 3 2 l o g ( x 2 + 3 3 x + 3 3 2 ) + 6 3 3 l o g ( x 2 + 3 3 x + 3 3 2 ) + 3 3 6 5 atan ( 3 2 6 3 x + 3 3 ) + 6 3 atan ( 3 2 6 3 x + 3 3 )
Por lo tanto, el resultado es: − 3 3 log ( x − 3 3 ) 12 + 3 2 3 log ( x − 3 3 ) 12 + log ( x 3 − 3 ) 12 − 3 2 3 log ( x 2 + 3 3 x + 3 2 3 ) 24 + 3 3 log ( x 2 + 3 3 x + 3 2 3 ) 24 + 3 5 6 atan ( 2 3 6 x 3 + 3 3 ) 12 + 3 6 atan ( 2 3 6 x 3 + 3 3 ) 4 - \frac{\sqrt[3]{3} \log{\left(x - \sqrt[3]{3} \right)}}{12} + \frac{3^{\frac{2}{3}} \log{\left(x - \sqrt[3]{3} \right)}}{12} + \frac{\log{\left(x^{3} - 3 \right)}}{12} - \frac{3^{\frac{2}{3}} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{24} + \frac{\sqrt[3]{3} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{24} + \frac{3^{\frac{5}{6}} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{12} + \frac{\sqrt[6]{3} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{4} − 12 3 3 l o g ( x − 3 3 ) + 12 3 3 2 l o g ( x − 3 3 ) + 12 l o g ( x 3 − 3 ) − 24 3 3 2 l o g ( x 2 + 3 3 x + 3 3 2 ) + 24 3 3 l o g ( x 2 + 3 3 x + 3 3 2 ) + 12 3 6 5 atan ( 3 2 6 3 x + 3 3 ) + 4 6 3 atan ( 3 2 6 3 x + 3 3 )
La integral del producto de una función por una constante es la constante por la integral de esta función:
∫ ( − 1 4 ( x + 1 ) ) d x = − ∫ 1 x + 1 d x 4 \int \left(- \frac{1}{4 \left(x + 1\right)}\right)\, dx = - \frac{\int \frac{1}{x + 1}\, dx}{4} ∫ ( − 4 ( x + 1 ) 1 ) d x = − 4 ∫ x + 1 1 d x
que u = x + 1 u = x + 1 u = x + 1 .
Luego que d u = d x du = dx d u = d x y ponemos d u du d u :
∫ 1 u d u \int \frac{1}{u}\, du ∫ u 1 d u
Integral 1 u \frac{1}{u} u 1 es log ( u ) \log{\left(u \right)} log ( u ) .
Si ahora sustituir u u u más en:
log ( x + 1 ) \log{\left(x + 1 \right)} log ( x + 1 )
Por lo tanto, el resultado es: − log ( x + 1 ) 4 - \frac{\log{\left(x + 1 \right)}}{4} − 4 l o g ( x + 1 )
El resultado es: − log ( x + 1 ) 4 − 3 3 log ( x − 3 3 ) 12 + 3 2 3 log ( x − 3 3 ) 12 + log ( x 3 − 3 ) 12 − 3 2 3 log ( x 2 + 3 3 x + 3 2 3 ) 24 + 3 3 log ( x 2 + 3 3 x + 3 2 3 ) 24 + 3 5 6 atan ( 2 3 6 x 3 + 3 3 ) 12 + 3 6 atan ( 2 3 6 x 3 + 3 3 ) 4 - \frac{\log{\left(x + 1 \right)}}{4} - \frac{\sqrt[3]{3} \log{\left(x - \sqrt[3]{3} \right)}}{12} + \frac{3^{\frac{2}{3}} \log{\left(x - \sqrt[3]{3} \right)}}{12} + \frac{\log{\left(x^{3} - 3 \right)}}{12} - \frac{3^{\frac{2}{3}} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{24} + \frac{\sqrt[3]{3} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{24} + \frac{3^{\frac{5}{6}} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{12} + \frac{\sqrt[6]{3} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{4} − 4 l o g ( x + 1 ) − 12 3 3 l o g ( x − 3 3 ) + 12 3 3 2 l o g ( x − 3 3 ) + 12 l o g ( x 3 − 3 ) − 24 3 3 2 l o g ( x 2 + 3 3 x + 3 3 2 ) + 24 3 3 l o g ( x 2 + 3 3 x + 3 3 2 ) + 12 3 6 5 atan ( 3 2 6 3 x + 3 3 ) + 4 6 3 atan ( 3 2 6 3 x + 3 3 )
Por lo tanto, el resultado es: − 5 log ( x + 1 ) − 5 3 3 log ( x − 3 3 ) 3 + 5 ⋅ 3 2 3 log ( x − 3 3 ) 3 + 5 log ( x 3 − 3 ) 3 − 5 ⋅ 3 2 3 log ( x 2 + 3 3 x + 3 2 3 ) 6 + 5 3 3 log ( x 2 + 3 3 x + 3 2 3 ) 6 + 5 ⋅ 3 5 6 atan ( 2 3 6 x 3 + 3 3 ) 3 + 5 3 6 atan ( 2 3 6 x 3 + 3 3 ) - 5 \log{\left(x + 1 \right)} - \frac{5 \sqrt[3]{3} \log{\left(x - \sqrt[3]{3} \right)}}{3} + \frac{5 \cdot 3^{\frac{2}{3}} \log{\left(x - \sqrt[3]{3} \right)}}{3} + \frac{5 \log{\left(x^{3} - 3 \right)}}{3} - \frac{5 \cdot 3^{\frac{2}{3}} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \frac{5 \sqrt[3]{3} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \frac{5 \cdot 3^{\frac{5}{6}} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{3} + 5 \sqrt[6]{3} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)} − 5 log ( x + 1 ) − 3 5 3 3 l o g ( x − 3 3 ) + 3 5 ⋅ 3 3 2 l o g ( x − 3 3 ) + 3 5 l o g ( x 3 − 3 ) − 6 5 ⋅ 3 3 2 l o g ( x 2 + 3 3 x + 3 3 2 ) + 6 5 3 3 l o g ( x 2 + 3 3 x + 3 3 2 ) + 3 5 ⋅ 3 6 5 atan ( 3 2 6 3 x + 3 3 ) + 5 6 3 atan ( 3 2 6 3 x + 3 3 )
Añadimos la constante de integración:
− 5 log ( x + 1 ) − 5 3 3 log ( x − 3 3 ) 3 + 5 ⋅ 3 2 3 log ( x − 3 3 ) 3 + 5 log ( x 3 − 3 ) 3 − 5 ⋅ 3 2 3 log ( x 2 + 3 3 x + 3 2 3 ) 6 + 5 3 3 log ( x 2 + 3 3 x + 3 2 3 ) 6 + 5 ⋅ 3 5 6 atan ( 2 3 6 x 3 + 3 3 ) 3 + 5 3 6 atan ( 2 3 6 x 3 + 3 3 ) + c o n s t a n t - 5 \log{\left(x + 1 \right)} - \frac{5 \sqrt[3]{3} \log{\left(x - \sqrt[3]{3} \right)}}{3} + \frac{5 \cdot 3^{\frac{2}{3}} \log{\left(x - \sqrt[3]{3} \right)}}{3} + \frac{5 \log{\left(x^{3} - 3 \right)}}{3} - \frac{5 \cdot 3^{\frac{2}{3}} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \frac{5 \sqrt[3]{3} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \frac{5 \cdot 3^{\frac{5}{6}} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{3} + 5 \sqrt[6]{3} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}+ \mathrm{constant} − 5 log ( x + 1 ) − 3 5 3 3 l o g ( x − 3 3 ) + 3 5 ⋅ 3 3 2 l o g ( x − 3 3 ) + 3 5 l o g ( x 3 − 3 ) − 6 5 ⋅ 3 3 2 l o g ( x 2 + 3 3 x + 3 3 2 ) + 6 5 3 3 l o g ( x 2 + 3 3 x + 3 3 2 ) + 3 5 ⋅ 3 6 5 atan ( 3 2 6 3 x + 3 3 ) + 5 6 3 atan ( 3 2 6 3 x + 3 3 ) + constant
Respuesta:
− 5 log ( x + 1 ) − 5 3 3 log ( x − 3 3 ) 3 + 5 ⋅ 3 2 3 log ( x − 3 3 ) 3 + 5 log ( x 3 − 3 ) 3 − 5 ⋅ 3 2 3 log ( x 2 + 3 3 x + 3 2 3 ) 6 + 5 3 3 log ( x 2 + 3 3 x + 3 2 3 ) 6 + 5 ⋅ 3 5 6 atan ( 2 3 6 x 3 + 3 3 ) 3 + 5 3 6 atan ( 2 3 6 x 3 + 3 3 ) + c o n s t a n t - 5 \log{\left(x + 1 \right)} - \frac{5 \sqrt[3]{3} \log{\left(x - \sqrt[3]{3} \right)}}{3} + \frac{5 \cdot 3^{\frac{2}{3}} \log{\left(x - \sqrt[3]{3} \right)}}{3} + \frac{5 \log{\left(x^{3} - 3 \right)}}{3} - \frac{5 \cdot 3^{\frac{2}{3}} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \frac{5 \sqrt[3]{3} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \frac{5 \cdot 3^{\frac{5}{6}} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{3} + 5 \sqrt[6]{3} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}+ \mathrm{constant} − 5 log ( x + 1 ) − 3 5 3 3 l o g ( x − 3 3 ) + 3 5 ⋅ 3 3 2 l o g ( x − 3 3 ) + 3 5 l o g ( x 3 − 3 ) − 6 5 ⋅ 3 3 2 l o g ( x 2 + 3 3 x + 3 3 2 ) + 6 5 3 3 l o g ( x 2 + 3 3 x + 3 3 2 ) + 3 5 ⋅ 3 6 5 atan ( 3 2 6 3 x + 3 3 ) + 5 6 3 atan ( 3 2 6 3 x + 3 3 ) + constant
Respuesta (Indefinida)
[src]
/ / ___ 6 ___\
| 5/6 |\/ 3 2*x*\/ 3 |
| 2 / 3\ / ___ 6 ___\ 3 ___ / 3 ___\ 2/3 / 2/3 2 3 ___\ 2/3 / 3 ___\ 5*3 *atan|----- + ---------| 3 ___ / 2/3 2 3 ___\
| 20*x 5*log\-3 + x / 6 ___ |\/ 3 2*x*\/ 3 | 5*\/ 3 *log\x - \/ 3 / 5*3 *log\3 + x + x*\/ 3 / 5*3 *log\x - \/ 3 / \ 3 3 / 5*\/ 3 *log\3 + x + x*\/ 3 /
| ------------------ dx = C - 5*log(1 + x) + -------------- + 5*\/ 3 *atan|----- + ---------| - ---------------------- - ------------------------------- + --------------------- + ------------------------------ + --------------------------------
| / 2 \ 3 \ 3 3 / 3 6 3 3 6
| \x *x - 3/*(x + 1)
|
/
∫ 20 x 2 ( x + 1 ) ( x x 2 − 3 ) d x = C − 5 log ( x + 1 ) − 5 3 3 log ( x − 3 3 ) 3 + 5 ⋅ 3 2 3 log ( x − 3 3 ) 3 + 5 log ( x 3 − 3 ) 3 − 5 ⋅ 3 2 3 log ( x 2 + 3 3 x + 3 2 3 ) 6 + 5 3 3 log ( x 2 + 3 3 x + 3 2 3 ) 6 + 5 ⋅ 3 5 6 atan ( 2 3 6 x 3 + 3 3 ) 3 + 5 3 6 atan ( 2 3 6 x 3 + 3 3 ) \int \frac{20 x^{2}}{\left(x + 1\right) \left(x x^{2} - 3\right)}\, dx = C - 5 \log{\left(x + 1 \right)} - \frac{5 \sqrt[3]{3} \log{\left(x - \sqrt[3]{3} \right)}}{3} + \frac{5 \cdot 3^{\frac{2}{3}} \log{\left(x - \sqrt[3]{3} \right)}}{3} + \frac{5 \log{\left(x^{3} - 3 \right)}}{3} - \frac{5 \cdot 3^{\frac{2}{3}} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \frac{5 \sqrt[3]{3} \log{\left(x^{2} + \sqrt[3]{3} x + 3^{\frac{2}{3}} \right)}}{6} + \frac{5 \cdot 3^{\frac{5}{6}} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)}}{3} + 5 \sqrt[6]{3} \operatorname{atan}{\left(\frac{2 \sqrt[6]{3} x}{3} + \frac{\sqrt{3}}{3} \right)} ∫ ( x + 1 ) ( x x 2 − 3 ) 20 x 2 d x = C − 5 log ( x + 1 ) − 3 5 3 3 log ( x − 3 3 ) + 3 5 ⋅ 3 3 2 log ( x − 3 3 ) + 3 5 log ( x 3 − 3 ) − 6 5 ⋅ 3 3 2 log ( x 2 + 3 3 x + 3 3 2 ) + 6 5 3 3 log ( x 2 + 3 3 x + 3 3 2 ) + 3 5 ⋅ 3 6 5 atan ( 3 2 6 3 x + 3 3 ) + 5 6 3 atan ( 3 2 6 3 x + 3 3 )
Gráfica
0.00 1.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 5 -10
/ / 2 3\\ / / 2 3\\
__________________________________________ | | / 3 ___ 2/3\ / 3 ___ 2/3\ || | | / 3 ___ 2/3\ / 3 ___ 2/3\ || __________________________________________
/ _______________ / _______________ _______________ _______________ \ | | |1 \/ 3 3 | |1 \/ 3 3 | || / _______________ _______________ _______________\ | | |1 \/ 3 3 | |1 \/ 3 3 | || / _______________ _______________ _______________\ / _______________ / _______________ _______________ _______________ \
/ / 2/3 3 ___ / 3 ___\ | 2/3 / 2/3 3 ___ 2/3 / 2/3 3 ___ / 2/3 | | | 3 ___ 2/3 288*|-- - ----- + ----| 6480*|-- - ----- + ----| || / 3 ___ 2/3\ / 2/3 3 ___\ | 3 ___ / 2/3 2/3 3 ___ / 2/3 2/3 / 2/3 | | | 3 ___ 2/3 288*|-- - ----- + ----| 6480*|-- - ----- + ----| || / 3 ___ 2/3\ / 2/3 3 ___\ | 3 ___ / 2/3 2/3 3 ___ / 2/3 2/3 / 2/3 | / / 2/3 3 ___ / 3 ___\ | 2/3 / 2/3 3 ___ 2/3 / 2/3 3 ___ / 2/3 |
/ \/ -15 + 16*3 \/ 3 *\7 - 3*\/ 3 / | 1726 39*3 318*\/ -15 + 16*3 1465*\/ 3 135*3 *\/ -15 + 16*3 135*\/ 3 *\/ -15 + 16*3 | | |205 21*\/ 3 21*3 \12 12 12 / \12 12 12 / || |1 \/ 3 3 | |1 3 \/ 3 | |975663 1732071*\/ 3 178059*\/ -15 + 16*3 345431*3 15207*\/ 3 *\/ -15 + 16*3 162369*3 *\/ -15 + 16*3 | | | 7 21*\/ 3 21*3 \12 12 12 / \12 12 12 / || |1 \/ 3 3 | |1 3 \/ 3 | |747763 1421491*\/ 3 144351*\/ -15 + 16*3 353699*3 43827*\/ 3 *\/ -15 + 16*3 133749*3 *\/ -15 + 16*3 | / \/ -15 + 16*3 \/ 3 *\7 - 3*\/ 3 / | 2574 39*3 318*\/ -15 + 16*3 1465*\/ 3 135*3 *\/ -15 + 16*3 135*\/ 3 *\/ -15 + 16*3 |
-5*log(2) - 40* / ------------------ + ------------------- *atan|- ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - 20*|pi*I + log|--- - -------- + ------- + ------------------------ + -------------------------||*|-- - ----- + ----| - 20*|-- - ---- + -----|*log|------ - ------------- - ------------------------- + ----------- + ------------------------------ + ------------------------------| + 20*|pi*I + log|- --- - -------- + ------- + ------------------------ + -------------------------||*|-- - ----- + ----| + 20*|-- - ---- + -----|*log|------ - ------------- - ------------------------- + ----------- + ------------------------------ + ------------------------------| + 40* / ------------------ + ------------------- *atan|- ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
\/ 96 192 | ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________| \ \212 212 212 53 53 // \12 12 12 / \12 24 24 / \44944 89888 44944 89888 89888 89888 / \ \ 212 212 212 53 53 // \12 12 12 / \12 24 24 / \44944 89888 44944 89888 89888 89888 / \/ 96 192 | ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________|
| / _______________ / _______________ / _______________ _______________ / _______________ / _______________ / _______________ / _______________ _______________ / _______________ / _______________ / _______________ / _______________ _______________ / _______________ / _______________ / _______________ / _______________ _______________ / _______________ / _______________ / _______________ / _______________ _______________ / _______________ / _______________ / _______________ / _______________ _______________ / _______________ | | / _______________ / _______________ / _______________ _______________ / _______________ / _______________ / _______________ / _______________ _______________ / _______________ / _______________ / _______________ / _______________ _______________ / _______________ / _______________ / _______________ / _______________ _______________ / _______________ / _______________ / _______________ / _______________ _______________ / _______________ / _______________ / _______________ / _______________ _______________ / _______________ |
| 6 ___ / 2/3 / 2/3 3 ___ 5/6 / 2/3 / 2/3 3 ___ ___ / 2/3 / 2/3 3 ___ ___ / 2/3 / 2/3 / 2/3 3 ___ 6 ___ / 2/3 / 2/3 3 ___ 5/6 / 2/3 / 2/3 3 ___ ___ / 2/3 / 2/3 3 ___ ___ / 2/3 / 2/3 / 2/3 3 ___ 6 ___ / 2/3 / 2/3 3 ___ 5/6 / 2/3 / 2/3 3 ___ ___ / 2/3 / 2/3 3 ___ ___ / 2/3 / 2/3 / 2/3 3 ___ 6 ___ / 2/3 / 2/3 3 ___ 5/6 / 2/3 / 2/3 3 ___ ___ / 2/3 / 2/3 3 ___ ___ / 2/3 / 2/3 / 2/3 3 ___ 6 ___ / 2/3 / 2/3 3 ___ 5/6 / 2/3 / 2/3 3 ___ ___ / 2/3 / 2/3 3 ___ ___ / 2/3 / 2/3 / 2/3 3 ___ 6 ___ / 2/3 / 2/3 3 ___ 5/6 / 2/3 / 2/3 3 ___ ___ / 2/3 / 2/3 3 ___ ___ / 2/3 / 2/3 / 2/3 3 ___ | | 6 ___ / 2/3 / 2/3 3 ___ 5/6 / 2/3 / 2/3 3 ___ ___ / 2/3 / 2/3 3 ___ ___ / 2/3 / 2/3 / 2/3 3 ___ 6 ___ / 2/3 / 2/3 3 ___ 5/6 / 2/3 / 2/3 3 ___ ___ / 2/3 / 2/3 3 ___ ___ / 2/3 / 2/3 / 2/3 3 ___ 6 ___ / 2/3 / 2/3 3 ___ 5/6 / 2/3 / 2/3 3 ___ ___ / 2/3 / 2/3 3 ___ ___ / 2/3 / 2/3 / 2/3 3 ___ 6 ___ / 2/3 / 2/3 3 ___ 5/6 / 2/3 / 2/3 3 ___ ___ / 2/3 / 2/3 3 ___ ___ / 2/3 / 2/3 / 2/3 3 ___ 6 ___ / 2/3 / 2/3 3 ___ 5/6 / 2/3 / 2/3 3 ___ ___ / 2/3 / 2/3 3 ___ ___ / 2/3 / 2/3 / 2/3 3 ___ 6 ___ / 2/3 / 2/3 3 ___ 5/6 / 2/3 / 2/3 3 ___ ___ / 2/3 / 2/3 3 ___ ___ / 2/3 / 2/3 / 2/3 3 ___ |
\ - 48*\/ 3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 + 16*3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 + 29*\/ 3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 - 45*\/ 3 *\/ -15 + 16*3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 - 48*\/ 3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 + 16*3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 + 29*\/ 3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 - 45*\/ 3 *\/ -15 + 16*3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 - 48*\/ 3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 + 16*3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 + 29*\/ 3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 - 45*\/ 3 *\/ -15 + 16*3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 - 48*\/ 3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 + 16*3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 + 29*\/ 3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 - 45*\/ 3 *\/ -15 + 16*3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 - 48*\/ 3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 + 16*3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 + 29*\/ 3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 - 45*\/ 3 *\/ -15 + 16*3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 - 48*\/ 3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 + 16*3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 + 29*\/ 3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 - 45*\/ 3 *\/ -15 + 16*3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 / \ - 48*\/ 3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 + 16*3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 + 29*\/ 3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 - 45*\/ 3 *\/ -15 + 16*3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 - 48*\/ 3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 + 16*3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 + 29*\/ 3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 - 45*\/ 3 *\/ -15 + 16*3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 - 48*\/ 3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 + 16*3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 + 29*\/ 3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 - 45*\/ 3 *\/ -15 + 16*3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 - 48*\/ 3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 + 16*3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 + 29*\/ 3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 - 45*\/ 3 *\/ -15 + 16*3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 - 48*\/ 3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 + 16*3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 + 29*\/ 3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 - 45*\/ 3 *\/ -15 + 16*3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 - 48*\/ 3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 + 16*3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 + 29*\/ 3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 - 45*\/ 3 *\/ -15 + 16*3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 /
40 3 3 ( 7 − 3 3 3 ) 192 + − 15 + 16 ⋅ 3 2 3 96 atan ( 1465 3 3 − 45 3 − 15 + 16 ⋅ 3 2 3 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 − 48 3 6 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 16 ⋅ 3 5 6 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 29 3 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 318 − 15 + 16 ⋅ 3 2 3 − 45 3 − 15 + 16 ⋅ 3 2 3 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 − 48 3 6 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 16 ⋅ 3 5 6 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 29 3 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 135 3 3 − 15 + 16 ⋅ 3 2 3 − 45 3 − 15 + 16 ⋅ 3 2 3 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 − 48 3 6 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 16 ⋅ 3 5 6 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 29 3 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 39 ⋅ 3 2 3 − 45 3 − 15 + 16 ⋅ 3 2 3 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 − 48 3 6 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 16 ⋅ 3 5 6 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 29 3 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 − 135 ⋅ 3 2 3 − 15 + 16 ⋅ 3 2 3 − 45 3 − 15 + 16 ⋅ 3 2 3 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 − 48 3 6 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 16 ⋅ 3 5 6 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 29 3 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 − 2574 − 45 3 − 15 + 16 ⋅ 3 2 3 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 − 48 3 6 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 16 ⋅ 3 5 6 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 29 3 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 ) − 5 log ( 2 ) − 20 ( − 3 2 3 24 + 3 3 24 + 1 12 ) log ( − 1732071 3 3 89888 − 178059 − 15 + 16 ⋅ 3 2 3 44944 + 15207 3 3 − 15 + 16 ⋅ 3 2 3 89888 + 345431 ⋅ 3 2 3 89888 + 162369 ⋅ 3 2 3 − 15 + 16 ⋅ 3 2 3 89888 + 975663 44944 ) + 20 ( − 3 2 3 24 + 3 3 24 + 1 12 ) log ( − 1421491 3 3 89888 − 144351 − 15 + 16 ⋅ 3 2 3 44944 + 43827 3 3 − 15 + 16 ⋅ 3 2 3 89888 + 353699 ⋅ 3 2 3 89888 + 133749 ⋅ 3 2 3 − 15 + 16 ⋅ 3 2 3 89888 + 747763 44944 ) − 40 3 3 ( 7 − 3 3 3 ) 192 + − 15 + 16 ⋅ 3 2 3 96 atan ( 1465 3 3 − 45 3 − 15 + 16 ⋅ 3 2 3 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 − 48 3 6 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 16 ⋅ 3 5 6 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 29 3 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 318 − 15 + 16 ⋅ 3 2 3 − 45 3 − 15 + 16 ⋅ 3 2 3 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 − 48 3 6 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 16 ⋅ 3 5 6 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 29 3 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 135 3 3 − 15 + 16 ⋅ 3 2 3 − 45 3 − 15 + 16 ⋅ 3 2 3 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 − 48 3 6 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 16 ⋅ 3 5 6 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 29 3 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 39 ⋅ 3 2 3 − 45 3 − 15 + 16 ⋅ 3 2 3 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 − 48 3 6 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 16 ⋅ 3 5 6 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 29 3 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 − 135 ⋅ 3 2 3 − 15 + 16 ⋅ 3 2 3 − 45 3 − 15 + 16 ⋅ 3 2 3 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 − 48 3 6 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 16 ⋅ 3 5 6 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 29 3 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 − 1726 − 45 3 − 15 + 16 ⋅ 3 2 3 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 − 48 3 6 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 16 ⋅ 3 5 6 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 29 3 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 ) − 20 ( log ( − 21 3 3 212 + 288 ( − 3 3 12 + 1 12 + 3 2 3 12 ) 2 53 + 21 ⋅ 3 2 3 212 + 6480 ( − 3 3 12 + 1 12 + 3 2 3 12 ) 3 53 + 205 212 ) + i π ) ( − 3 3 12 + 1 12 + 3 2 3 12 ) + 20 ( log ( − 21 3 3 212 − 7 212 + 288 ( − 3 3 12 + 1 12 + 3 2 3 12 ) 2 53 + 21 ⋅ 3 2 3 212 + 6480 ( − 3 3 12 + 1 12 + 3 2 3 12 ) 3 53 ) + i π ) ( − 3 3 12 + 1 12 + 3 2 3 12 ) 40 \sqrt{\frac{\sqrt[3]{3} \left(7 - 3 \sqrt[3]{3}\right)}{192} + \frac{\sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}}}{96}} \operatorname{atan}{\left(\frac{1465 \sqrt[3]{3}}{- 45 \sqrt{3} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} - 48 \sqrt[6]{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 16 \cdot 3^{\frac{5}{6}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 29 \sqrt{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}}} + \frac{318 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}}}{- 45 \sqrt{3} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} - 48 \sqrt[6]{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 16 \cdot 3^{\frac{5}{6}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 29 \sqrt{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}}} + \frac{135 \sqrt[3]{3} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}}}{- 45 \sqrt{3} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} - 48 \sqrt[6]{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 16 \cdot 3^{\frac{5}{6}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 29 \sqrt{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}}} + \frac{39 \cdot 3^{\frac{2}{3}}}{- 45 \sqrt{3} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} - 48 \sqrt[6]{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 16 \cdot 3^{\frac{5}{6}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 29 \sqrt{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}}} - \frac{135 \cdot 3^{\frac{2}{3}} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}}}{- 45 \sqrt{3} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} - 48 \sqrt[6]{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 16 \cdot 3^{\frac{5}{6}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 29 \sqrt{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}}} - \frac{2574}{- 45 \sqrt{3} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} - 48 \sqrt[6]{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 16 \cdot 3^{\frac{5}{6}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 29 \sqrt{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}}} \right)} - 5 \log{\left(2 \right)} - 20 \left(- \frac{3^{\frac{2}{3}}}{24} + \frac{\sqrt[3]{3}}{24} + \frac{1}{12}\right) \log{\left(- \frac{1732071 \sqrt[3]{3}}{89888} - \frac{178059 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}}}{44944} + \frac{15207 \sqrt[3]{3} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}}}{89888} + \frac{345431 \cdot 3^{\frac{2}{3}}}{89888} + \frac{162369 \cdot 3^{\frac{2}{3}} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}}}{89888} + \frac{975663}{44944} \right)} + 20 \left(- \frac{3^{\frac{2}{3}}}{24} + \frac{\sqrt[3]{3}}{24} + \frac{1}{12}\right) \log{\left(- \frac{1421491 \sqrt[3]{3}}{89888} - \frac{144351 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}}}{44944} + \frac{43827 \sqrt[3]{3} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}}}{89888} + \frac{353699 \cdot 3^{\frac{2}{3}}}{89888} + \frac{133749 \cdot 3^{\frac{2}{3}} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}}}{89888} + \frac{747763}{44944} \right)} - 40 \sqrt{\frac{\sqrt[3]{3} \left(7 - 3 \sqrt[3]{3}\right)}{192} + \frac{\sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}}}{96}} \operatorname{atan}{\left(\frac{1465 \sqrt[3]{3}}{- 45 \sqrt{3} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} - 48 \sqrt[6]{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 16 \cdot 3^{\frac{5}{6}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 29 \sqrt{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}}} + \frac{318 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}}}{- 45 \sqrt{3} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} - 48 \sqrt[6]{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 16 \cdot 3^{\frac{5}{6}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 29 \sqrt{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}}} + \frac{135 \sqrt[3]{3} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}}}{- 45 \sqrt{3} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} - 48 \sqrt[6]{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 16 \cdot 3^{\frac{5}{6}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 29 \sqrt{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}}} + \frac{39 \cdot 3^{\frac{2}{3}}}{- 45 \sqrt{3} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} - 48 \sqrt[6]{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 16 \cdot 3^{\frac{5}{6}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 29 \sqrt{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}}} - \frac{135 \cdot 3^{\frac{2}{3}} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}}}{- 45 \sqrt{3} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} - 48 \sqrt[6]{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 16 \cdot 3^{\frac{5}{6}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 29 \sqrt{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}}} - \frac{1726}{- 45 \sqrt{3} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} - 48 \sqrt[6]{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 16 \cdot 3^{\frac{5}{6}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 29 \sqrt{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}}} \right)} - 20 \left(\log{\left(- \frac{21 \sqrt[3]{3}}{212} + \frac{288 \left(- \frac{\sqrt[3]{3}}{12} + \frac{1}{12} + \frac{3^{\frac{2}{3}}}{12}\right)^{2}}{53} + \frac{21 \cdot 3^{\frac{2}{3}}}{212} + \frac{6480 \left(- \frac{\sqrt[3]{3}}{12} + \frac{1}{12} + \frac{3^{\frac{2}{3}}}{12}\right)^{3}}{53} + \frac{205}{212} \right)} + i \pi\right) \left(- \frac{\sqrt[3]{3}}{12} + \frac{1}{12} + \frac{3^{\frac{2}{3}}}{12}\right) + 20 \left(\log{\left(- \frac{21 \sqrt[3]{3}}{212} - \frac{7}{212} + \frac{288 \left(- \frac{\sqrt[3]{3}}{12} + \frac{1}{12} + \frac{3^{\frac{2}{3}}}{12}\right)^{2}}{53} + \frac{21 \cdot 3^{\frac{2}{3}}}{212} + \frac{6480 \left(- \frac{\sqrt[3]{3}}{12} + \frac{1}{12} + \frac{3^{\frac{2}{3}}}{12}\right)^{3}}{53} \right)} + i \pi\right) \left(- \frac{\sqrt[3]{3}}{12} + \frac{1}{12} + \frac{3^{\frac{2}{3}}}{12}\right) 40 192 3 3 ( 7 − 3 3 3 ) + 96 − 15 + 16 ⋅ 3 3 2 atan − 45 3 − 15 + 16 ⋅ 3 3 2 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 − 48 6 3 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 + 16 ⋅ 3 6 5 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 + 29 3 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 1465 3 3 + − 45 3 − 15 + 16 ⋅ 3 3 2 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 − 48 6 3 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 + 16 ⋅ 3 6 5 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 + 29 3 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 318 − 15 + 16 ⋅ 3 3 2 + − 45 3 − 15 + 16 ⋅ 3 3 2 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 − 48 6 3 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 + 16 ⋅ 3 6 5 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 + 29 3 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 135 3 3 − 15 + 16 ⋅ 3 3 2 + − 45 3 − 15 + 16 ⋅ 3 3 2 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 − 48 6 3 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 + 16 ⋅ 3 6 5 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 + 29 3 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 39 ⋅ 3 3 2 − − 45 3 − 15 + 16 ⋅ 3 3 2 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 − 48 6 3 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 + 16 ⋅ 3 6 5 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 + 29 3 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 135 ⋅ 3 3 2 − 15 + 16 ⋅ 3 3 2 − − 45 3 − 15 + 16 ⋅ 3 3 2 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 − 48 6 3 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 + 16 ⋅ 3 6 5 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 + 29 3 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 2574 − 5 log ( 2 ) − 20 ( − 24 3 3 2 + 24 3 3 + 12 1 ) log ( − 89888 1732071 3 3 − 44944 178059 − 15 + 16 ⋅ 3 3 2 + 89888 15207 3 3 − 15 + 16 ⋅ 3 3 2 + 89888 345431 ⋅ 3 3 2 + 89888 162369 ⋅ 3 3 2 − 15 + 16 ⋅ 3 3 2 + 44944 975663 ) + 20 ( − 24 3 3 2 + 24 3 3 + 12 1 ) log ( − 89888 1421491 3 3 − 44944 144351 − 15 + 16 ⋅ 3 3 2 + 89888 43827 3 3 − 15 + 16 ⋅ 3 3 2 + 89888 353699 ⋅ 3 3 2 + 89888 133749 ⋅ 3 3 2 − 15 + 16 ⋅ 3 3 2 + 44944 747763 ) − 40 192 3 3 ( 7 − 3 3 3 ) + 96 − 15 + 16 ⋅ 3 3 2 atan − 45 3 − 15 + 16 ⋅ 3 3 2 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 − 48 6 3 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 + 16 ⋅ 3 6 5 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 + 29 3 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 1465 3 3 + − 45 3 − 15 + 16 ⋅ 3 3 2 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 − 48 6 3 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 + 16 ⋅ 3 6 5 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 + 29 3 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 318 − 15 + 16 ⋅ 3 3 2 + − 45 3 − 15 + 16 ⋅ 3 3 2 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 − 48 6 3 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 + 16 ⋅ 3 6 5 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 + 29 3 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 135 3 3 − 15 + 16 ⋅ 3 3 2 + − 45 3 − 15 + 16 ⋅ 3 3 2 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 − 48 6 3 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 + 16 ⋅ 3 6 5 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 + 29 3 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 39 ⋅ 3 3 2 − − 45 3 − 15 + 16 ⋅ 3 3 2 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 − 48 6 3 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 + 16 ⋅ 3 6 5 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 + 29 3 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 135 ⋅ 3 3 2 − 15 + 16 ⋅ 3 3 2 − − 45 3 − 15 + 16 ⋅ 3 3 2 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 − 48 6 3 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 + 16 ⋅ 3 6 5 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 + 29 3 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 1726 − 20 log − 212 21 3 3 + 53 288 ( − 12 3 3 + 12 1 + 12 3 3 2 ) 2 + 212 21 ⋅ 3 3 2 + 53 6480 ( − 12 3 3 + 12 1 + 12 3 3 2 ) 3 + 212 205 + iπ ( − 12 3 3 + 12 1 + 12 3 3 2 ) + 20 log − 212 21 3 3 − 212 7 + 53 288 ( − 12 3 3 + 12 1 + 12 3 3 2 ) 2 + 212 21 ⋅ 3 3 2 + 53 6480 ( − 12 3 3 + 12 1 + 12 3 3 2 ) 3 + iπ ( − 12 3 3 + 12 1 + 12 3 3 2 )
=
/ / 2 3\\ / / 2 3\\
__________________________________________ | | / 3 ___ 2/3\ / 3 ___ 2/3\ || | | / 3 ___ 2/3\ / 3 ___ 2/3\ || __________________________________________
/ _______________ / _______________ _______________ _______________ \ | | |1 \/ 3 3 | |1 \/ 3 3 | || / _______________ _______________ _______________\ | | |1 \/ 3 3 | |1 \/ 3 3 | || / _______________ _______________ _______________\ / _______________ / _______________ _______________ _______________ \
/ / 2/3 3 ___ / 3 ___\ | 2/3 / 2/3 3 ___ 2/3 / 2/3 3 ___ / 2/3 | | | 3 ___ 2/3 288*|-- - ----- + ----| 6480*|-- - ----- + ----| || / 3 ___ 2/3\ / 2/3 3 ___\ | 3 ___ / 2/3 2/3 3 ___ / 2/3 2/3 / 2/3 | | | 3 ___ 2/3 288*|-- - ----- + ----| 6480*|-- - ----- + ----| || / 3 ___ 2/3\ / 2/3 3 ___\ | 3 ___ / 2/3 2/3 3 ___ / 2/3 2/3 / 2/3 | / / 2/3 3 ___ / 3 ___\ | 2/3 / 2/3 3 ___ 2/3 / 2/3 3 ___ / 2/3 |
/ \/ -15 + 16*3 \/ 3 *\7 - 3*\/ 3 / | 1726 39*3 318*\/ -15 + 16*3 1465*\/ 3 135*3 *\/ -15 + 16*3 135*\/ 3 *\/ -15 + 16*3 | | |205 21*\/ 3 21*3 \12 12 12 / \12 12 12 / || |1 \/ 3 3 | |1 3 \/ 3 | |975663 1732071*\/ 3 178059*\/ -15 + 16*3 345431*3 15207*\/ 3 *\/ -15 + 16*3 162369*3 *\/ -15 + 16*3 | | | 7 21*\/ 3 21*3 \12 12 12 / \12 12 12 / || |1 \/ 3 3 | |1 3 \/ 3 | |747763 1421491*\/ 3 144351*\/ -15 + 16*3 353699*3 43827*\/ 3 *\/ -15 + 16*3 133749*3 *\/ -15 + 16*3 | / \/ -15 + 16*3 \/ 3 *\7 - 3*\/ 3 / | 2574 39*3 318*\/ -15 + 16*3 1465*\/ 3 135*3 *\/ -15 + 16*3 135*\/ 3 *\/ -15 + 16*3 |
-5*log(2) - 40* / ------------------ + ------------------- *atan|- ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - 20*|pi*I + log|--- - -------- + ------- + ------------------------ + -------------------------||*|-- - ----- + ----| - 20*|-- - ---- + -----|*log|------ - ------------- - ------------------------- + ----------- + ------------------------------ + ------------------------------| + 20*|pi*I + log|- --- - -------- + ------- + ------------------------ + -------------------------||*|-- - ----- + ----| + 20*|-- - ---- + -----|*log|------ - ------------- - ------------------------- + ----------- + ------------------------------ + ------------------------------| + 40* / ------------------ + ------------------- *atan|- ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
\/ 96 192 | ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________| \ \212 212 212 53 53 // \12 12 12 / \12 24 24 / \44944 89888 44944 89888 89888 89888 / \ \ 212 212 212 53 53 // \12 12 12 / \12 24 24 / \44944 89888 44944 89888 89888 89888 / \/ 96 192 | ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________ ___________________________________________|
| / _______________ / _______________ / _______________ _______________ / _______________ / _______________ / _______________ / _______________ _______________ / _______________ / _______________ / _______________ / _______________ _______________ / _______________ / _______________ / _______________ / _______________ _______________ / _______________ / _______________ / _______________ / _______________ _______________ / _______________ / _______________ / _______________ / _______________ _______________ / _______________ | | / _______________ / _______________ / _______________ _______________ / _______________ / _______________ / _______________ / _______________ _______________ / _______________ / _______________ / _______________ / _______________ _______________ / _______________ / _______________ / _______________ / _______________ _______________ / _______________ / _______________ / _______________ / _______________ _______________ / _______________ / _______________ / _______________ / _______________ _______________ / _______________ |
| 6 ___ / 2/3 / 2/3 3 ___ 5/6 / 2/3 / 2/3 3 ___ ___ / 2/3 / 2/3 3 ___ ___ / 2/3 / 2/3 / 2/3 3 ___ 6 ___ / 2/3 / 2/3 3 ___ 5/6 / 2/3 / 2/3 3 ___ ___ / 2/3 / 2/3 3 ___ ___ / 2/3 / 2/3 / 2/3 3 ___ 6 ___ / 2/3 / 2/3 3 ___ 5/6 / 2/3 / 2/3 3 ___ ___ / 2/3 / 2/3 3 ___ ___ / 2/3 / 2/3 / 2/3 3 ___ 6 ___ / 2/3 / 2/3 3 ___ 5/6 / 2/3 / 2/3 3 ___ ___ / 2/3 / 2/3 3 ___ ___ / 2/3 / 2/3 / 2/3 3 ___ 6 ___ / 2/3 / 2/3 3 ___ 5/6 / 2/3 / 2/3 3 ___ ___ / 2/3 / 2/3 3 ___ ___ / 2/3 / 2/3 / 2/3 3 ___ 6 ___ / 2/3 / 2/3 3 ___ 5/6 / 2/3 / 2/3 3 ___ ___ / 2/3 / 2/3 3 ___ ___ / 2/3 / 2/3 / 2/3 3 ___ | | 6 ___ / 2/3 / 2/3 3 ___ 5/6 / 2/3 / 2/3 3 ___ ___ / 2/3 / 2/3 3 ___ ___ / 2/3 / 2/3 / 2/3 3 ___ 6 ___ / 2/3 / 2/3 3 ___ 5/6 / 2/3 / 2/3 3 ___ ___ / 2/3 / 2/3 3 ___ ___ / 2/3 / 2/3 / 2/3 3 ___ 6 ___ / 2/3 / 2/3 3 ___ 5/6 / 2/3 / 2/3 3 ___ ___ / 2/3 / 2/3 3 ___ ___ / 2/3 / 2/3 / 2/3 3 ___ 6 ___ / 2/3 / 2/3 3 ___ 5/6 / 2/3 / 2/3 3 ___ ___ / 2/3 / 2/3 3 ___ ___ / 2/3 / 2/3 / 2/3 3 ___ 6 ___ / 2/3 / 2/3 3 ___ 5/6 / 2/3 / 2/3 3 ___ ___ / 2/3 / 2/3 3 ___ ___ / 2/3 / 2/3 / 2/3 3 ___ 6 ___ / 2/3 / 2/3 3 ___ 5/6 / 2/3 / 2/3 3 ___ ___ / 2/3 / 2/3 3 ___ ___ / 2/3 / 2/3 / 2/3 3 ___ |
\ - 48*\/ 3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 + 16*3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 + 29*\/ 3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 - 45*\/ 3 *\/ -15 + 16*3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 - 48*\/ 3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 + 16*3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 + 29*\/ 3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 - 45*\/ 3 *\/ -15 + 16*3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 - 48*\/ 3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 + 16*3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 + 29*\/ 3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 - 45*\/ 3 *\/ -15 + 16*3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 - 48*\/ 3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 + 16*3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 + 29*\/ 3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 - 45*\/ 3 *\/ -15 + 16*3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 - 48*\/ 3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 + 16*3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 + 29*\/ 3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 - 45*\/ 3 *\/ -15 + 16*3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 - 48*\/ 3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 + 16*3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 + 29*\/ 3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 - 45*\/ 3 *\/ -15 + 16*3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 / \ - 48*\/ 3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 + 16*3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 + 29*\/ 3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 - 45*\/ 3 *\/ -15 + 16*3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 - 48*\/ 3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 + 16*3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 + 29*\/ 3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 - 45*\/ 3 *\/ -15 + 16*3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 - 48*\/ 3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 + 16*3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 + 29*\/ 3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 - 45*\/ 3 *\/ -15 + 16*3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 - 48*\/ 3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 + 16*3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 + 29*\/ 3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 - 45*\/ 3 *\/ -15 + 16*3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 - 48*\/ 3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 + 16*3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 + 29*\/ 3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 - 45*\/ 3 *\/ -15 + 16*3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 - 48*\/ 3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 + 16*3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 + 29*\/ 3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 - 45*\/ 3 *\/ -15 + 16*3 *\/ - 3*3 + 2*\/ -15 + 16*3 + 7*\/ 3 /
40 3 3 ( 7 − 3 3 3 ) 192 + − 15 + 16 ⋅ 3 2 3 96 atan ( 1465 3 3 − 45 3 − 15 + 16 ⋅ 3 2 3 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 − 48 3 6 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 16 ⋅ 3 5 6 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 29 3 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 318 − 15 + 16 ⋅ 3 2 3 − 45 3 − 15 + 16 ⋅ 3 2 3 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 − 48 3 6 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 16 ⋅ 3 5 6 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 29 3 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 135 3 3 − 15 + 16 ⋅ 3 2 3 − 45 3 − 15 + 16 ⋅ 3 2 3 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 − 48 3 6 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 16 ⋅ 3 5 6 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 29 3 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 39 ⋅ 3 2 3 − 45 3 − 15 + 16 ⋅ 3 2 3 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 − 48 3 6 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 16 ⋅ 3 5 6 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 29 3 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 − 135 ⋅ 3 2 3 − 15 + 16 ⋅ 3 2 3 − 45 3 − 15 + 16 ⋅ 3 2 3 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 − 48 3 6 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 16 ⋅ 3 5 6 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 29 3 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 − 2574 − 45 3 − 15 + 16 ⋅ 3 2 3 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 − 48 3 6 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 16 ⋅ 3 5 6 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 29 3 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 ) − 5 log ( 2 ) − 20 ( − 3 2 3 24 + 3 3 24 + 1 12 ) log ( − 1732071 3 3 89888 − 178059 − 15 + 16 ⋅ 3 2 3 44944 + 15207 3 3 − 15 + 16 ⋅ 3 2 3 89888 + 345431 ⋅ 3 2 3 89888 + 162369 ⋅ 3 2 3 − 15 + 16 ⋅ 3 2 3 89888 + 975663 44944 ) + 20 ( − 3 2 3 24 + 3 3 24 + 1 12 ) log ( − 1421491 3 3 89888 − 144351 − 15 + 16 ⋅ 3 2 3 44944 + 43827 3 3 − 15 + 16 ⋅ 3 2 3 89888 + 353699 ⋅ 3 2 3 89888 + 133749 ⋅ 3 2 3 − 15 + 16 ⋅ 3 2 3 89888 + 747763 44944 ) − 40 3 3 ( 7 − 3 3 3 ) 192 + − 15 + 16 ⋅ 3 2 3 96 atan ( 1465 3 3 − 45 3 − 15 + 16 ⋅ 3 2 3 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 − 48 3 6 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 16 ⋅ 3 5 6 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 29 3 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 318 − 15 + 16 ⋅ 3 2 3 − 45 3 − 15 + 16 ⋅ 3 2 3 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 − 48 3 6 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 16 ⋅ 3 5 6 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 29 3 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 135 3 3 − 15 + 16 ⋅ 3 2 3 − 45 3 − 15 + 16 ⋅ 3 2 3 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 − 48 3 6 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 16 ⋅ 3 5 6 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 29 3 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 39 ⋅ 3 2 3 − 45 3 − 15 + 16 ⋅ 3 2 3 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 − 48 3 6 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 16 ⋅ 3 5 6 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 29 3 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 − 135 ⋅ 3 2 3 − 15 + 16 ⋅ 3 2 3 − 45 3 − 15 + 16 ⋅ 3 2 3 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 − 48 3 6 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 16 ⋅ 3 5 6 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 29 3 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 − 1726 − 45 3 − 15 + 16 ⋅ 3 2 3 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 − 48 3 6 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 16 ⋅ 3 5 6 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 + 29 3 − 3 ⋅ 3 2 3 + 2 − 15 + 16 ⋅ 3 2 3 + 7 3 3 ) − 20 ( log ( − 21 3 3 212 + 288 ( − 3 3 12 + 1 12 + 3 2 3 12 ) 2 53 + 21 ⋅ 3 2 3 212 + 6480 ( − 3 3 12 + 1 12 + 3 2 3 12 ) 3 53 + 205 212 ) + i π ) ( − 3 3 12 + 1 12 + 3 2 3 12 ) + 20 ( log ( − 21 3 3 212 − 7 212 + 288 ( − 3 3 12 + 1 12 + 3 2 3 12 ) 2 53 + 21 ⋅ 3 2 3 212 + 6480 ( − 3 3 12 + 1 12 + 3 2 3 12 ) 3 53 ) + i π ) ( − 3 3 12 + 1 12 + 3 2 3 12 ) 40 \sqrt{\frac{\sqrt[3]{3} \left(7 - 3 \sqrt[3]{3}\right)}{192} + \frac{\sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}}}{96}} \operatorname{atan}{\left(\frac{1465 \sqrt[3]{3}}{- 45 \sqrt{3} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} - 48 \sqrt[6]{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 16 \cdot 3^{\frac{5}{6}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 29 \sqrt{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}}} + \frac{318 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}}}{- 45 \sqrt{3} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} - 48 \sqrt[6]{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 16 \cdot 3^{\frac{5}{6}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 29 \sqrt{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}}} + \frac{135 \sqrt[3]{3} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}}}{- 45 \sqrt{3} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} - 48 \sqrt[6]{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 16 \cdot 3^{\frac{5}{6}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 29 \sqrt{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}}} + \frac{39 \cdot 3^{\frac{2}{3}}}{- 45 \sqrt{3} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} - 48 \sqrt[6]{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 16 \cdot 3^{\frac{5}{6}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 29 \sqrt{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}}} - \frac{135 \cdot 3^{\frac{2}{3}} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}}}{- 45 \sqrt{3} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} - 48 \sqrt[6]{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 16 \cdot 3^{\frac{5}{6}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 29 \sqrt{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}}} - \frac{2574}{- 45 \sqrt{3} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} - 48 \sqrt[6]{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 16 \cdot 3^{\frac{5}{6}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 29 \sqrt{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}}} \right)} - 5 \log{\left(2 \right)} - 20 \left(- \frac{3^{\frac{2}{3}}}{24} + \frac{\sqrt[3]{3}}{24} + \frac{1}{12}\right) \log{\left(- \frac{1732071 \sqrt[3]{3}}{89888} - \frac{178059 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}}}{44944} + \frac{15207 \sqrt[3]{3} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}}}{89888} + \frac{345431 \cdot 3^{\frac{2}{3}}}{89888} + \frac{162369 \cdot 3^{\frac{2}{3}} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}}}{89888} + \frac{975663}{44944} \right)} + 20 \left(- \frac{3^{\frac{2}{3}}}{24} + \frac{\sqrt[3]{3}}{24} + \frac{1}{12}\right) \log{\left(- \frac{1421491 \sqrt[3]{3}}{89888} - \frac{144351 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}}}{44944} + \frac{43827 \sqrt[3]{3} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}}}{89888} + \frac{353699 \cdot 3^{\frac{2}{3}}}{89888} + \frac{133749 \cdot 3^{\frac{2}{3}} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}}}{89888} + \frac{747763}{44944} \right)} - 40 \sqrt{\frac{\sqrt[3]{3} \left(7 - 3 \sqrt[3]{3}\right)}{192} + \frac{\sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}}}{96}} \operatorname{atan}{\left(\frac{1465 \sqrt[3]{3}}{- 45 \sqrt{3} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} - 48 \sqrt[6]{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 16 \cdot 3^{\frac{5}{6}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 29 \sqrt{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}}} + \frac{318 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}}}{- 45 \sqrt{3} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} - 48 \sqrt[6]{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 16 \cdot 3^{\frac{5}{6}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 29 \sqrt{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}}} + \frac{135 \sqrt[3]{3} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}}}{- 45 \sqrt{3} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} - 48 \sqrt[6]{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 16 \cdot 3^{\frac{5}{6}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 29 \sqrt{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}}} + \frac{39 \cdot 3^{\frac{2}{3}}}{- 45 \sqrt{3} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} - 48 \sqrt[6]{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 16 \cdot 3^{\frac{5}{6}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 29 \sqrt{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}}} - \frac{135 \cdot 3^{\frac{2}{3}} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}}}{- 45 \sqrt{3} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} - 48 \sqrt[6]{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 16 \cdot 3^{\frac{5}{6}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 29 \sqrt{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}}} - \frac{1726}{- 45 \sqrt{3} \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} - 48 \sqrt[6]{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 16 \cdot 3^{\frac{5}{6}} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}} + 29 \sqrt{3} \sqrt{- 3 \cdot 3^{\frac{2}{3}} + 2 \sqrt{-15 + 16 \cdot 3^{\frac{2}{3}}} + 7 \sqrt[3]{3}}} \right)} - 20 \left(\log{\left(- \frac{21 \sqrt[3]{3}}{212} + \frac{288 \left(- \frac{\sqrt[3]{3}}{12} + \frac{1}{12} + \frac{3^{\frac{2}{3}}}{12}\right)^{2}}{53} + \frac{21 \cdot 3^{\frac{2}{3}}}{212} + \frac{6480 \left(- \frac{\sqrt[3]{3}}{12} + \frac{1}{12} + \frac{3^{\frac{2}{3}}}{12}\right)^{3}}{53} + \frac{205}{212} \right)} + i \pi\right) \left(- \frac{\sqrt[3]{3}}{12} + \frac{1}{12} + \frac{3^{\frac{2}{3}}}{12}\right) + 20 \left(\log{\left(- \frac{21 \sqrt[3]{3}}{212} - \frac{7}{212} + \frac{288 \left(- \frac{\sqrt[3]{3}}{12} + \frac{1}{12} + \frac{3^{\frac{2}{3}}}{12}\right)^{2}}{53} + \frac{21 \cdot 3^{\frac{2}{3}}}{212} + \frac{6480 \left(- \frac{\sqrt[3]{3}}{12} + \frac{1}{12} + \frac{3^{\frac{2}{3}}}{12}\right)^{3}}{53} \right)} + i \pi\right) \left(- \frac{\sqrt[3]{3}}{12} + \frac{1}{12} + \frac{3^{\frac{2}{3}}}{12}\right) 40 192 3 3 ( 7 − 3 3 3 ) + 96 − 15 + 16 ⋅ 3 3 2 atan − 45 3 − 15 + 16 ⋅ 3 3 2 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 − 48 6 3 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 + 16 ⋅ 3 6 5 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 + 29 3 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 1465 3 3 + − 45 3 − 15 + 16 ⋅ 3 3 2 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 − 48 6 3 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 + 16 ⋅ 3 6 5 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 + 29 3 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 318 − 15 + 16 ⋅ 3 3 2 + − 45 3 − 15 + 16 ⋅ 3 3 2 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 − 48 6 3 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 + 16 ⋅ 3 6 5 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 + 29 3 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 135 3 3 − 15 + 16 ⋅ 3 3 2 + − 45 3 − 15 + 16 ⋅ 3 3 2 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 − 48 6 3 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 + 16 ⋅ 3 6 5 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 + 29 3 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 39 ⋅ 3 3 2 − − 45 3 − 15 + 16 ⋅ 3 3 2 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 − 48 6 3 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 + 16 ⋅ 3 6 5 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 + 29 3 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 135 ⋅ 3 3 2 − 15 + 16 ⋅ 3 3 2 − − 45 3 − 15 + 16 ⋅ 3 3 2 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 − 48 6 3 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 + 16 ⋅ 3 6 5 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 + 29 3 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 2574 − 5 log ( 2 ) − 20 ( − 24 3 3 2 + 24 3 3 + 12 1 ) log ( − 89888 1732071 3 3 − 44944 178059 − 15 + 16 ⋅ 3 3 2 + 89888 15207 3 3 − 15 + 16 ⋅ 3 3 2 + 89888 345431 ⋅ 3 3 2 + 89888 162369 ⋅ 3 3 2 − 15 + 16 ⋅ 3 3 2 + 44944 975663 ) + 20 ( − 24 3 3 2 + 24 3 3 + 12 1 ) log ( − 89888 1421491 3 3 − 44944 144351 − 15 + 16 ⋅ 3 3 2 + 89888 43827 3 3 − 15 + 16 ⋅ 3 3 2 + 89888 353699 ⋅ 3 3 2 + 89888 133749 ⋅ 3 3 2 − 15 + 16 ⋅ 3 3 2 + 44944 747763 ) − 40 192 3 3 ( 7 − 3 3 3 ) + 96 − 15 + 16 ⋅ 3 3 2 atan − 45 3 − 15 + 16 ⋅ 3 3 2 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 − 48 6 3 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 + 16 ⋅ 3 6 5 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 + 29 3 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 1465 3 3 + − 45 3 − 15 + 16 ⋅ 3 3 2 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 − 48 6 3 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 + 16 ⋅ 3 6 5 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 + 29 3 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 318 − 15 + 16 ⋅ 3 3 2 + − 45 3 − 15 + 16 ⋅ 3 3 2 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 − 48 6 3 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 + 16 ⋅ 3 6 5 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 + 29 3 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 135 3 3 − 15 + 16 ⋅ 3 3 2 + − 45 3 − 15 + 16 ⋅ 3 3 2 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 − 48 6 3 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 + 16 ⋅ 3 6 5 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 + 29 3 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 39 ⋅ 3 3 2 − − 45 3 − 15 + 16 ⋅ 3 3 2 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 − 48 6 3 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 + 16 ⋅ 3 6 5 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 + 29 3 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 135 ⋅ 3 3 2 − 15 + 16 ⋅ 3 3 2 − − 45 3 − 15 + 16 ⋅ 3 3 2 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 − 48 6 3 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 + 16 ⋅ 3 6 5 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 + 29 3 − 3 ⋅ 3 3 2 + 2 − 15 + 16 ⋅ 3 3 2 + 7 3 3 1726 − 20 log − 212 21 3 3 + 53 288 ( − 12 3 3 + 12 1 + 12 3 3 2 ) 2 + 212 21 ⋅ 3 3 2 + 53 6480 ( − 12 3 3 + 12 1 + 12 3 3 2 ) 3 + 212 205 + iπ ( − 12 3 3 + 12 1 + 12 3 3 2 ) + 20 log − 212 21 3 3 − 212 7 + 53 288 ( − 12 3 3 + 12 1 + 12 3 3 2 ) 2 + 212 21 ⋅ 3 3 2 + 53 6480 ( − 12 3 3 + 12 1 + 12 3 3 2 ) 3 + iπ ( − 12 3 3 + 12 1 + 12 3 3 2 )
-5*log(2) - 40*sqrt(sqrt(-15 + 16*3^(2/3))/96 + 3^(1/3)*(7 - 3*3^(1/3))/192)*atan(-1726/(-48*3^(1/6)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) + 16*3^(5/6)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) + 29*sqrt(3)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) - 45*sqrt(3)*sqrt(-15 + 16*3^(2/3))*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3))) + 39*3^(2/3)/(-48*3^(1/6)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) + 16*3^(5/6)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) + 29*sqrt(3)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) - 45*sqrt(3)*sqrt(-15 + 16*3^(2/3))*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3))) + 318*sqrt(-15 + 16*3^(2/3))/(-48*3^(1/6)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) + 16*3^(5/6)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) + 29*sqrt(3)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) - 45*sqrt(3)*sqrt(-15 + 16*3^(2/3))*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3))) + 1465*3^(1/3)/(-48*3^(1/6)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) + 16*3^(5/6)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) + 29*sqrt(3)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) - 45*sqrt(3)*sqrt(-15 + 16*3^(2/3))*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3))) - 135*3^(2/3)*sqrt(-15 + 16*3^(2/3))/(-48*3^(1/6)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) + 16*3^(5/6)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) + 29*sqrt(3)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) - 45*sqrt(3)*sqrt(-15 + 16*3^(2/3))*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3))) + 135*3^(1/3)*sqrt(-15 + 16*3^(2/3))/(-48*3^(1/6)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) + 16*3^(5/6)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) + 29*sqrt(3)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) - 45*sqrt(3)*sqrt(-15 + 16*3^(2/3))*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)))) - 20*(pi*i + log(205/212 - 21*3^(1/3)/212 + 21*3^(2/3)/212 + 288*(1/12 - 3^(1/3)/12 + 3^(2/3)/12)^2/53 + 6480*(1/12 - 3^(1/3)/12 + 3^(2/3)/12)^3/53))*(1/12 - 3^(1/3)/12 + 3^(2/3)/12) - 20*(1/12 - 3^(2/3)/24 + 3^(1/3)/24)*log(975663/44944 - 1732071*3^(1/3)/89888 - 178059*sqrt(-15 + 16*3^(2/3))/44944 + 345431*3^(2/3)/89888 + 15207*3^(1/3)*sqrt(-15 + 16*3^(2/3))/89888 + 162369*3^(2/3)*sqrt(-15 + 16*3^(2/3))/89888) + 20*(pi*i + log(-7/212 - 21*3^(1/3)/212 + 21*3^(2/3)/212 + 288*(1/12 - 3^(1/3)/12 + 3^(2/3)/12)^2/53 + 6480*(1/12 - 3^(1/3)/12 + 3^(2/3)/12)^3/53))*(1/12 - 3^(1/3)/12 + 3^(2/3)/12) + 20*(1/12 - 3^(2/3)/24 + 3^(1/3)/24)*log(747763/44944 - 1421491*3^(1/3)/89888 - 144351*sqrt(-15 + 16*3^(2/3))/44944 + 353699*3^(2/3)/89888 + 43827*3^(1/3)*sqrt(-15 + 16*3^(2/3))/89888 + 133749*3^(2/3)*sqrt(-15 + 16*3^(2/3))/89888) + 40*sqrt(sqrt(-15 + 16*3^(2/3))/96 + 3^(1/3)*(7 - 3*3^(1/3))/192)*atan(-2574/(-48*3^(1/6)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) + 16*3^(5/6)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) + 29*sqrt(3)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) - 45*sqrt(3)*sqrt(-15 + 16*3^(2/3))*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3))) + 39*3^(2/3)/(-48*3^(1/6)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) + 16*3^(5/6)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) + 29*sqrt(3)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) - 45*sqrt(3)*sqrt(-15 + 16*3^(2/3))*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3))) + 318*sqrt(-15 + 16*3^(2/3))/(-48*3^(1/6)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) + 16*3^(5/6)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) + 29*sqrt(3)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) - 45*sqrt(3)*sqrt(-15 + 16*3^(2/3))*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3))) + 1465*3^(1/3)/(-48*3^(1/6)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) + 16*3^(5/6)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) + 29*sqrt(3)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) - 45*sqrt(3)*sqrt(-15 + 16*3^(2/3))*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3))) - 135*3^(2/3)*sqrt(-15 + 16*3^(2/3))/(-48*3^(1/6)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) + 16*3^(5/6)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) + 29*sqrt(3)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) - 45*sqrt(3)*sqrt(-15 + 16*3^(2/3))*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3))) + 135*3^(1/3)*sqrt(-15 + 16*3^(2/3))/(-48*3^(1/6)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) + 16*3^(5/6)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) + 29*sqrt(3)*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3)) - 45*sqrt(3)*sqrt(-15 + 16*3^(2/3))*sqrt(-3*3^(2/3) + 2*sqrt(-15 + 16*3^(2/3)) + 7*3^(1/3))))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.