Integral de 1/(А-tgx^2)(1/2) dx
Solución
Solución detallada
La integral del producto de una función por una constante es la constante por la integral de esta función:
∫ 1 2 ( a − tan 2 ( x ) ) d x = ∫ 1 a − tan 2 ( x ) d x 2 \int \frac{1}{2 \left(a - \tan^{2}{\left(x \right)}\right)}\, dx = \frac{\int \frac{1}{a - \tan^{2}{\left(x \right)}}\, dx}{2} ∫ 2 ( a − t a n 2 ( x ) ) 1 d x = 2 ∫ a − t a n 2 ( x ) 1 d x
No puedo encontrar los pasos en la búsqueda de esta integral.
Pero la integral
{ − x tan 2 ( x ) 2 tan 2 ( x ) + 2 − x 2 tan 2 ( x ) + 2 − tan ( x ) 2 tan 2 ( x ) + 2 for a = − 1 x + 1 tan ( x ) for a = 0 2 a 5 2 x 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a + 4 a 3 2 x 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a + 2 a x 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a − a 2 log ( − a + tan ( x ) ) 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a + a 2 log ( a + tan ( x ) ) 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a − 2 a log ( − a + tan ( x ) ) 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a + 2 a log ( a + tan ( x ) ) 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a − log ( − a + tan ( x ) ) 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a + log ( a + tan ( x ) ) 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a otherwese \begin{cases} - \frac{x \tan^{2}{\left(x \right)}}{2 \tan^{2}{\left(x \right)} + 2} - \frac{x}{2 \tan^{2}{\left(x \right)} + 2} - \frac{\tan{\left(x \right)}}{2 \tan^{2}{\left(x \right)} + 2} & \text{for}\: a = -1 \\x + \frac{1}{\tan{\left(x \right)}} & \text{for}\: a = 0 \\\frac{2 a^{\frac{5}{2}} x}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} + \frac{4 a^{\frac{3}{2}} x}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} + \frac{2 \sqrt{a} x}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} - \frac{a^{2} \log{\left(- \sqrt{a} + \tan{\left(x \right)} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} + \frac{a^{2} \log{\left(\sqrt{a} + \tan{\left(x \right)} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} - \frac{2 a \log{\left(- \sqrt{a} + \tan{\left(x \right)} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} + \frac{2 a \log{\left(\sqrt{a} + \tan{\left(x \right)} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} - \frac{\log{\left(- \sqrt{a} + \tan{\left(x \right)} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} + \frac{\log{\left(\sqrt{a} + \tan{\left(x \right)} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} & \text{otherwese} \end{cases} ⎩ ⎨ ⎧ − 2 t a n 2 ( x ) + 2 x t a n 2 ( x ) − 2 t a n 2 ( x ) + 2 x − 2 t a n 2 ( x ) + 2 t a n ( x ) x + t a n ( x ) 1 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a 2 a 2 5 x + 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a 4 a 2 3 x + 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a 2 a x − 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a a 2 l o g ( − a + t a n ( x ) ) + 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a a 2 l o g ( a + t a n ( x ) ) − 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a 2 a l o g ( − a + t a n ( x ) ) + 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a 2 a l o g ( a + t a n ( x ) ) − 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a l o g ( − a + t a n ( x ) ) + 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a l o g ( a + t a n ( x ) ) for a = − 1 for a = 0 otherwese
Por lo tanto, el resultado es: { − x tan 2 ( x ) 2 tan 2 ( x ) + 2 − x 2 tan 2 ( x ) + 2 − tan ( x ) 2 tan 2 ( x ) + 2 for a = − 1 x + 1 tan ( x ) for a = 0 2 a 5 2 x 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a + 4 a 3 2 x 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a + 2 a x 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a − a 2 log ( − a + tan ( x ) ) 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a + a 2 log ( a + tan ( x ) ) 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a − 2 a log ( − a + tan ( x ) ) 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a + 2 a log ( a + tan ( x ) ) 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a − log ( − a + tan ( x ) ) 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a + log ( a + tan ( x ) ) 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a otherwese 2 \frac{\begin{cases} - \frac{x \tan^{2}{\left(x \right)}}{2 \tan^{2}{\left(x \right)} + 2} - \frac{x}{2 \tan^{2}{\left(x \right)} + 2} - \frac{\tan{\left(x \right)}}{2 \tan^{2}{\left(x \right)} + 2} & \text{for}\: a = -1 \\x + \frac{1}{\tan{\left(x \right)}} & \text{for}\: a = 0 \\\frac{2 a^{\frac{5}{2}} x}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} + \frac{4 a^{\frac{3}{2}} x}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} + \frac{2 \sqrt{a} x}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} - \frac{a^{2} \log{\left(- \sqrt{a} + \tan{\left(x \right)} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} + \frac{a^{2} \log{\left(\sqrt{a} + \tan{\left(x \right)} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} - \frac{2 a \log{\left(- \sqrt{a} + \tan{\left(x \right)} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} + \frac{2 a \log{\left(\sqrt{a} + \tan{\left(x \right)} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} - \frac{\log{\left(- \sqrt{a} + \tan{\left(x \right)} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} + \frac{\log{\left(\sqrt{a} + \tan{\left(x \right)} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} & \text{otherwese} \end{cases}}{2} 2 ⎩ ⎨ ⎧ − 2 t a n 2 ( x ) + 2 x t a n 2 ( x ) − 2 t a n 2 ( x ) + 2 x − 2 t a n 2 ( x ) + 2 t a n ( x ) x + t a n ( x ) 1 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a 2 a 2 5 x + 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a 4 a 2 3 x + 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a 2 a x − 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a a 2 l o g ( − a + t a n ( x ) ) + 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a a 2 l o g ( a + t a n ( x ) ) − 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a 2 a l o g ( − a + t a n ( x ) ) + 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a 2 a l o g ( a + t a n ( x ) ) − 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a l o g ( − a + t a n ( x ) ) + 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a l o g ( a + t a n ( x ) ) for a = − 1 for a = 0 otherwese
Ahora simplificar:
{ − 2 x + sin ( 2 x ) 8 for a = − 1 x + 1 tan ( x ) 2 for a = 0 2 a 5 2 x + 4 a 3 2 x + 2 a x − a 2 log ( − a + tan ( x ) ) + a 2 log ( a + tan ( x ) ) − 2 a log ( − a + tan ( x ) ) + 2 a log ( a + tan ( x ) ) − log ( − a + tan ( x ) ) + log ( a + tan ( x ) ) 4 a ( a + 1 ) 3 otherwese \begin{cases} - \frac{2 x + \sin{\left(2 x \right)}}{8} & \text{for}\: a = -1 \\\frac{x + \frac{1}{\tan{\left(x \right)}}}{2} & \text{for}\: a = 0 \\\frac{2 a^{\frac{5}{2}} x + 4 a^{\frac{3}{2}} x + 2 \sqrt{a} x - a^{2} \log{\left(- \sqrt{a} + \tan{\left(x \right)} \right)} + a^{2} \log{\left(\sqrt{a} + \tan{\left(x \right)} \right)} - 2 a \log{\left(- \sqrt{a} + \tan{\left(x \right)} \right)} + 2 a \log{\left(\sqrt{a} + \tan{\left(x \right)} \right)} - \log{\left(- \sqrt{a} + \tan{\left(x \right)} \right)} + \log{\left(\sqrt{a} + \tan{\left(x \right)} \right)}}{4 \sqrt{a} \left(a + 1\right)^{3}} & \text{otherwese} \end{cases} ⎩ ⎨ ⎧ − 8 2 x + s i n ( 2 x ) 2 x + t a n ( x ) 1 4 a ( a + 1 ) 3 2 a 2 5 x + 4 a 2 3 x + 2 a x − a 2 l o g ( − a + t a n ( x ) ) + a 2 l o g ( a + t a n ( x ) ) − 2 a l o g ( − a + t a n ( x ) ) + 2 a l o g ( a + t a n ( x ) ) − l o g ( − a + t a n ( x ) ) + l o g ( a + t a n ( x ) ) for a = − 1 for a = 0 otherwese
Añadimos la constante de integración:
{ − 2 x + sin ( 2 x ) 8 for a = − 1 x + 1 tan ( x ) 2 for a = 0 2 a 5 2 x + 4 a 3 2 x + 2 a x − a 2 log ( − a + tan ( x ) ) + a 2 log ( a + tan ( x ) ) − 2 a log ( − a + tan ( x ) ) + 2 a log ( a + tan ( x ) ) − log ( − a + tan ( x ) ) + log ( a + tan ( x ) ) 4 a ( a + 1 ) 3 otherwese + c o n s t a n t \begin{cases} - \frac{2 x + \sin{\left(2 x \right)}}{8} & \text{for}\: a = -1 \\\frac{x + \frac{1}{\tan{\left(x \right)}}}{2} & \text{for}\: a = 0 \\\frac{2 a^{\frac{5}{2}} x + 4 a^{\frac{3}{2}} x + 2 \sqrt{a} x - a^{2} \log{\left(- \sqrt{a} + \tan{\left(x \right)} \right)} + a^{2} \log{\left(\sqrt{a} + \tan{\left(x \right)} \right)} - 2 a \log{\left(- \sqrt{a} + \tan{\left(x \right)} \right)} + 2 a \log{\left(\sqrt{a} + \tan{\left(x \right)} \right)} - \log{\left(- \sqrt{a} + \tan{\left(x \right)} \right)} + \log{\left(\sqrt{a} + \tan{\left(x \right)} \right)}}{4 \sqrt{a} \left(a + 1\right)^{3}} & \text{otherwese} \end{cases}+ \mathrm{constant} ⎩ ⎨ ⎧ − 8 2 x + s i n ( 2 x ) 2 x + t a n ( x ) 1 4 a ( a + 1 ) 3 2 a 2 5 x + 4 a 2 3 x + 2 a x − a 2 l o g ( − a + t a n ( x ) ) + a 2 l o g ( a + t a n ( x ) ) − 2 a l o g ( − a + t a n ( x ) ) + 2 a l o g ( a + t a n ( x ) ) − l o g ( − a + t a n ( x ) ) + l o g ( a + t a n ( x ) ) for a = − 1 for a = 0 otherwese + constant
Respuesta:
{ − 2 x + sin ( 2 x ) 8 for a = − 1 x + 1 tan ( x ) 2 for a = 0 2 a 5 2 x + 4 a 3 2 x + 2 a x − a 2 log ( − a + tan ( x ) ) + a 2 log ( a + tan ( x ) ) − 2 a log ( − a + tan ( x ) ) + 2 a log ( a + tan ( x ) ) − log ( − a + tan ( x ) ) + log ( a + tan ( x ) ) 4 a ( a + 1 ) 3 otherwese + c o n s t a n t \begin{cases} - \frac{2 x + \sin{\left(2 x \right)}}{8} & \text{for}\: a = -1 \\\frac{x + \frac{1}{\tan{\left(x \right)}}}{2} & \text{for}\: a = 0 \\\frac{2 a^{\frac{5}{2}} x + 4 a^{\frac{3}{2}} x + 2 \sqrt{a} x - a^{2} \log{\left(- \sqrt{a} + \tan{\left(x \right)} \right)} + a^{2} \log{\left(\sqrt{a} + \tan{\left(x \right)} \right)} - 2 a \log{\left(- \sqrt{a} + \tan{\left(x \right)} \right)} + 2 a \log{\left(\sqrt{a} + \tan{\left(x \right)} \right)} - \log{\left(- \sqrt{a} + \tan{\left(x \right)} \right)} + \log{\left(\sqrt{a} + \tan{\left(x \right)} \right)}}{4 \sqrt{a} \left(a + 1\right)^{3}} & \text{otherwese} \end{cases}+ \mathrm{constant} ⎩ ⎨ ⎧ − 8 2 x + s i n ( 2 x ) 2 x + t a n ( x ) 1 4 a ( a + 1 ) 3 2 a 2 5 x + 4 a 2 3 x + 2 a x − a 2 l o g ( − a + t a n ( x ) ) + a 2 l o g ( a + t a n ( x ) ) − 2 a l o g ( − a + t a n ( x ) ) + 2 a l o g ( a + t a n ( x ) ) − l o g ( − a + t a n ( x ) ) + l o g ( a + t a n ( x ) ) for a = − 1 for a = 0 otherwese + constant
Respuesta (Indefinida)
[src]
/ 2
| x tan(x) x*tan (x)
| - ------------- - ------------- - ------------- for a = -1
| 2 2 2
| 2 + 2*tan (x) 2 + 2*tan (x) 2 + 2*tan (x)
|
| 1
< x + ------ for a = 0
| tan(x)
|
| / ___ \ / ___ \ 2 / ___ \ 2 / ___ \ / ___ \ / ___ \ ___ 5/2 3/2
| log\\/ a + tan(x)/ log\- \/ a + tan(x)/ a *log\\/ a + tan(x)/ a *log\- \/ a + tan(x)/ 2*a*log\- \/ a + tan(x)/ 2*a*log\\/ a + tan(x)/ 2*x*\/ a 2*x*a 4*x*a
/ |---------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- - ---------------------------------- + ---------------------------------- + ---------------------------------- + ---------------------------------- + ---------------------------------- otherwise
| | ___ 7/2 3/2 5/2 ___ 7/2 3/2 5/2 ___ 7/2 3/2 5/2 ___ 7/2 3/2 5/2 ___ 7/2 3/2 5/2 ___ 7/2 3/2 5/2 ___ 7/2 3/2 5/2 ___ 7/2 3/2 5/2 ___ 7/2 3/2 5/2
| 1 \2*\/ a + 2*a + 6*a + 6*a 2*\/ a + 2*a + 6*a + 6*a 2*\/ a + 2*a + 6*a + 6*a 2*\/ a + 2*a + 6*a + 6*a 2*\/ a + 2*a + 6*a + 6*a 2*\/ a + 2*a + 6*a + 6*a 2*\/ a + 2*a + 6*a + 6*a 2*\/ a + 2*a + 6*a + 6*a 2*\/ a + 2*a + 6*a + 6*a
| --------------- dx = C + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
| / 2 \ 2
| \a - tan (x)/*2
|
/
∫ 1 2 ( a − tan 2 ( x ) ) d x = C + { − x tan 2 ( x ) 2 tan 2 ( x ) + 2 − x 2 tan 2 ( x ) + 2 − tan ( x ) 2 tan 2 ( x ) + 2 for a = − 1 x + 1 tan ( x ) for a = 0 2 a 5 2 x 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a + 4 a 3 2 x 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a + 2 a x 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a − a 2 log ( − a + tan ( x ) ) 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a + a 2 log ( a + tan ( x ) ) 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a − 2 a log ( − a + tan ( x ) ) 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a + 2 a log ( a + tan ( x ) ) 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a − log ( − a + tan ( x ) ) 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a + log ( a + tan ( x ) ) 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a otherwise 2 \int \frac{1}{2 \left(a - \tan^{2}{\left(x \right)}\right)}\, dx = C + \frac{\begin{cases} - \frac{x \tan^{2}{\left(x \right)}}{2 \tan^{2}{\left(x \right)} + 2} - \frac{x}{2 \tan^{2}{\left(x \right)} + 2} - \frac{\tan{\left(x \right)}}{2 \tan^{2}{\left(x \right)} + 2} & \text{for}\: a = -1 \\x + \frac{1}{\tan{\left(x \right)}} & \text{for}\: a = 0 \\\frac{2 a^{\frac{5}{2}} x}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} + \frac{4 a^{\frac{3}{2}} x}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} + \frac{2 \sqrt{a} x}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} - \frac{a^{2} \log{\left(- \sqrt{a} + \tan{\left(x \right)} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} + \frac{a^{2} \log{\left(\sqrt{a} + \tan{\left(x \right)} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} - \frac{2 a \log{\left(- \sqrt{a} + \tan{\left(x \right)} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} + \frac{2 a \log{\left(\sqrt{a} + \tan{\left(x \right)} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} - \frac{\log{\left(- \sqrt{a} + \tan{\left(x \right)} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} + \frac{\log{\left(\sqrt{a} + \tan{\left(x \right)} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} & \text{otherwise} \end{cases}}{2} ∫ 2 ( a − tan 2 ( x ) ) 1 d x = C + 2 ⎩ ⎨ ⎧ − 2 t a n 2 ( x ) + 2 x t a n 2 ( x ) − 2 t a n 2 ( x ) + 2 x − 2 t a n 2 ( x ) + 2 t a n ( x ) x + t a n ( x ) 1 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a 2 a 2 5 x + 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a 4 a 2 3 x + 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a 2 a x − 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a a 2 l o g ( − a + t a n ( x ) ) + 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a a 2 l o g ( a + t a n ( x ) ) − 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a 2 a l o g ( − a + t a n ( x ) ) + 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a 2 a l o g ( a + t a n ( x ) ) − 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a l o g ( − a + t a n ( x ) ) + 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a l o g ( a + t a n ( x ) ) for a = − 1 for a = 0 otherwise
/ 2
| 1 tan (1) tan(1)
| - ----------------- - ----------------- - ----------------- for a = -1
| / 2 \ / 2 \ / 2 \
| 2*\2 + 2*tan (1)/ 2*\2 + 2*tan (1)/ 2*\2 + 2*tan (1)/
|
< -oo for a = 0
|
| ___ 5/2 / ___\ / ___ \ 3/2 / ___\ / ___ \ / ___\ / ___ \ 2 / ___\ 2 / ___ \ / ___\ / ___ \ 2 / ___\ 2 / ___ \
| \/ a a log\-\/ a / log\\/ a + tan(1)/ 2*a log\\/ a / log\- \/ a + tan(1)/ a*log\-\/ a / a*log\\/ a + tan(1)/ a *log\-\/ a / a *log\\/ a + tan(1)/ a*log\\/ a / a*log\- \/ a + tan(1)/ a *log\\/ a / a *log\- \/ a + tan(1)/
|---------------------------------- + ---------------------------------- + -------------------------------------- + -------------------------------------- + ---------------------------------- - -------------------------------------- - -------------------------------------- + ---------------------------------- + ---------------------------------- + -------------------------------------- + -------------------------------------- - ---------------------------------- - ---------------------------------- - -------------------------------------- - -------------------------------------- otherwise
| ___ 7/2 3/2 5/2 ___ 7/2 3/2 5/2 / ___ 7/2 3/2 5/2\ / ___ 7/2 3/2 5/2\ ___ 7/2 3/2 5/2 / ___ 7/2 3/2 5/2\ / ___ 7/2 3/2 5/2\ ___ 7/2 3/2 5/2 ___ 7/2 3/2 5/2 / ___ 7/2 3/2 5/2\ / ___ 7/2 3/2 5/2\ ___ 7/2 3/2 5/2 ___ 7/2 3/2 5/2 / ___ 7/2 3/2 5/2\ / ___ 7/2 3/2 5/2\
\2*\/ a + 2*a + 6*a + 6*a 2*\/ a + 2*a + 6*a + 6*a 2*\2*\/ a + 2*a + 6*a + 6*a / 2*\2*\/ a + 2*a + 6*a + 6*a / 2*\/ a + 2*a + 6*a + 6*a 2*\2*\/ a + 2*a + 6*a + 6*a / 2*\2*\/ a + 2*a + 6*a + 6*a / 2*\/ a + 2*a + 6*a + 6*a 2*\/ a + 2*a + 6*a + 6*a 2*\2*\/ a + 2*a + 6*a + 6*a / 2*\2*\/ a + 2*a + 6*a + 6*a / 2*\/ a + 2*a + 6*a + 6*a 2*\/ a + 2*a + 6*a + 6*a 2*\2*\/ a + 2*a + 6*a + 6*a / 2*\2*\/ a + 2*a + 6*a + 6*a /
{ − tan 2 ( 1 ) 2 ( 2 + 2 tan 2 ( 1 ) ) − tan ( 1 ) 2 ( 2 + 2 tan 2 ( 1 ) ) − 1 2 ( 2 + 2 tan 2 ( 1 ) ) for a = − 1 − ∞ for a = 0 a 5 2 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a + 2 a 3 2 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a + a 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a + a 2 log ( − a ) 2 ( 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a ) − a 2 log ( a ) 2 ( 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a ) − a 2 log ( − a + tan ( 1 ) ) 2 ( 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a ) + a 2 log ( a + tan ( 1 ) ) 2 ( 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a ) + a log ( − a ) 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a − a log ( a ) 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a − a log ( − a + tan ( 1 ) ) 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a + a log ( a + tan ( 1 ) ) 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a + log ( − a ) 2 ( 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a ) − log ( a ) 2 ( 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a ) − log ( − a + tan ( 1 ) ) 2 ( 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a ) + log ( a + tan ( 1 ) ) 2 ( 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a ) otherwise \begin{cases} - \frac{\tan^{2}{\left(1 \right)}}{2 \left(2 + 2 \tan^{2}{\left(1 \right)}\right)} - \frac{\tan{\left(1 \right)}}{2 \left(2 + 2 \tan^{2}{\left(1 \right)}\right)} - \frac{1}{2 \left(2 + 2 \tan^{2}{\left(1 \right)}\right)} & \text{for}\: a = -1 \\-\infty & \text{for}\: a = 0 \\\frac{a^{\frac{5}{2}}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} + \frac{2 a^{\frac{3}{2}}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} + \frac{\sqrt{a}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} + \frac{a^{2} \log{\left(- \sqrt{a} \right)}}{2 \left(2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}\right)} - \frac{a^{2} \log{\left(\sqrt{a} \right)}}{2 \left(2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}\right)} - \frac{a^{2} \log{\left(- \sqrt{a} + \tan{\left(1 \right)} \right)}}{2 \left(2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}\right)} + \frac{a^{2} \log{\left(\sqrt{a} + \tan{\left(1 \right)} \right)}}{2 \left(2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}\right)} + \frac{a \log{\left(- \sqrt{a} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} - \frac{a \log{\left(\sqrt{a} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} - \frac{a \log{\left(- \sqrt{a} + \tan{\left(1 \right)} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} + \frac{a \log{\left(\sqrt{a} + \tan{\left(1 \right)} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} + \frac{\log{\left(- \sqrt{a} \right)}}{2 \left(2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}\right)} - \frac{\log{\left(\sqrt{a} \right)}}{2 \left(2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}\right)} - \frac{\log{\left(- \sqrt{a} + \tan{\left(1 \right)} \right)}}{2 \left(2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}\right)} + \frac{\log{\left(\sqrt{a} + \tan{\left(1 \right)} \right)}}{2 \left(2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}\right)} & \text{otherwise} \end{cases} ⎩ ⎨ ⎧ − 2 ( 2 + 2 t a n 2 ( 1 ) ) t a n 2 ( 1 ) − 2 ( 2 + 2 t a n 2 ( 1 ) ) t a n ( 1 ) − 2 ( 2 + 2 t a n 2 ( 1 ) ) 1 − ∞ 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a a 2 5 + 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a 2 a 2 3 + 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a a + 2 ( 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a ) a 2 l o g ( − a ) − 2 ( 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a ) a 2 l o g ( a ) − 2 ( 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a ) a 2 l o g ( − a + t a n ( 1 ) ) + 2 ( 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a ) a 2 l o g ( a + t a n ( 1 ) ) + 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a a l o g ( − a ) − 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a a l o g ( a ) − 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a a l o g ( − a + t a n ( 1 ) ) + 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a a l o g ( a + t a n ( 1 ) ) + 2 ( 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a ) l o g ( − a ) − 2 ( 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a ) l o g ( a ) − 2 ( 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a ) l o g ( − a + t a n ( 1 ) ) + 2 ( 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a ) l o g ( a + t a n ( 1 ) ) for a = − 1 for a = 0 otherwise
=
/ 2
| 1 tan (1) tan(1)
| - ----------------- - ----------------- - ----------------- for a = -1
| / 2 \ / 2 \ / 2 \
| 2*\2 + 2*tan (1)/ 2*\2 + 2*tan (1)/ 2*\2 + 2*tan (1)/
|
< -oo for a = 0
|
| ___ 5/2 / ___\ / ___ \ 3/2 / ___\ / ___ \ / ___\ / ___ \ 2 / ___\ 2 / ___ \ / ___\ / ___ \ 2 / ___\ 2 / ___ \
| \/ a a log\-\/ a / log\\/ a + tan(1)/ 2*a log\\/ a / log\- \/ a + tan(1)/ a*log\-\/ a / a*log\\/ a + tan(1)/ a *log\-\/ a / a *log\\/ a + tan(1)/ a*log\\/ a / a*log\- \/ a + tan(1)/ a *log\\/ a / a *log\- \/ a + tan(1)/
|---------------------------------- + ---------------------------------- + -------------------------------------- + -------------------------------------- + ---------------------------------- - -------------------------------------- - -------------------------------------- + ---------------------------------- + ---------------------------------- + -------------------------------------- + -------------------------------------- - ---------------------------------- - ---------------------------------- - -------------------------------------- - -------------------------------------- otherwise
| ___ 7/2 3/2 5/2 ___ 7/2 3/2 5/2 / ___ 7/2 3/2 5/2\ / ___ 7/2 3/2 5/2\ ___ 7/2 3/2 5/2 / ___ 7/2 3/2 5/2\ / ___ 7/2 3/2 5/2\ ___ 7/2 3/2 5/2 ___ 7/2 3/2 5/2 / ___ 7/2 3/2 5/2\ / ___ 7/2 3/2 5/2\ ___ 7/2 3/2 5/2 ___ 7/2 3/2 5/2 / ___ 7/2 3/2 5/2\ / ___ 7/2 3/2 5/2\
\2*\/ a + 2*a + 6*a + 6*a 2*\/ a + 2*a + 6*a + 6*a 2*\2*\/ a + 2*a + 6*a + 6*a / 2*\2*\/ a + 2*a + 6*a + 6*a / 2*\/ a + 2*a + 6*a + 6*a 2*\2*\/ a + 2*a + 6*a + 6*a / 2*\2*\/ a + 2*a + 6*a + 6*a / 2*\/ a + 2*a + 6*a + 6*a 2*\/ a + 2*a + 6*a + 6*a 2*\2*\/ a + 2*a + 6*a + 6*a / 2*\2*\/ a + 2*a + 6*a + 6*a / 2*\/ a + 2*a + 6*a + 6*a 2*\/ a + 2*a + 6*a + 6*a 2*\2*\/ a + 2*a + 6*a + 6*a / 2*\2*\/ a + 2*a + 6*a + 6*a /
{ − tan 2 ( 1 ) 2 ( 2 + 2 tan 2 ( 1 ) ) − tan ( 1 ) 2 ( 2 + 2 tan 2 ( 1 ) ) − 1 2 ( 2 + 2 tan 2 ( 1 ) ) for a = − 1 − ∞ for a = 0 a 5 2 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a + 2 a 3 2 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a + a 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a + a 2 log ( − a ) 2 ( 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a ) − a 2 log ( a ) 2 ( 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a ) − a 2 log ( − a + tan ( 1 ) ) 2 ( 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a ) + a 2 log ( a + tan ( 1 ) ) 2 ( 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a ) + a log ( − a ) 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a − a log ( a ) 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a − a log ( − a + tan ( 1 ) ) 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a + a log ( a + tan ( 1 ) ) 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a + log ( − a ) 2 ( 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a ) − log ( a ) 2 ( 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a ) − log ( − a + tan ( 1 ) ) 2 ( 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a ) + log ( a + tan ( 1 ) ) 2 ( 2 a 7 2 + 6 a 5 2 + 6 a 3 2 + 2 a ) otherwise \begin{cases} - \frac{\tan^{2}{\left(1 \right)}}{2 \left(2 + 2 \tan^{2}{\left(1 \right)}\right)} - \frac{\tan{\left(1 \right)}}{2 \left(2 + 2 \tan^{2}{\left(1 \right)}\right)} - \frac{1}{2 \left(2 + 2 \tan^{2}{\left(1 \right)}\right)} & \text{for}\: a = -1 \\-\infty & \text{for}\: a = 0 \\\frac{a^{\frac{5}{2}}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} + \frac{2 a^{\frac{3}{2}}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} + \frac{\sqrt{a}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} + \frac{a^{2} \log{\left(- \sqrt{a} \right)}}{2 \left(2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}\right)} - \frac{a^{2} \log{\left(\sqrt{a} \right)}}{2 \left(2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}\right)} - \frac{a^{2} \log{\left(- \sqrt{a} + \tan{\left(1 \right)} \right)}}{2 \left(2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}\right)} + \frac{a^{2} \log{\left(\sqrt{a} + \tan{\left(1 \right)} \right)}}{2 \left(2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}\right)} + \frac{a \log{\left(- \sqrt{a} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} - \frac{a \log{\left(\sqrt{a} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} - \frac{a \log{\left(- \sqrt{a} + \tan{\left(1 \right)} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} + \frac{a \log{\left(\sqrt{a} + \tan{\left(1 \right)} \right)}}{2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}} + \frac{\log{\left(- \sqrt{a} \right)}}{2 \left(2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}\right)} - \frac{\log{\left(\sqrt{a} \right)}}{2 \left(2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}\right)} - \frac{\log{\left(- \sqrt{a} + \tan{\left(1 \right)} \right)}}{2 \left(2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}\right)} + \frac{\log{\left(\sqrt{a} + \tan{\left(1 \right)} \right)}}{2 \left(2 a^{\frac{7}{2}} + 6 a^{\frac{5}{2}} + 6 a^{\frac{3}{2}} + 2 \sqrt{a}\right)} & \text{otherwise} \end{cases} ⎩ ⎨ ⎧ − 2 ( 2 + 2 t a n 2 ( 1 ) ) t a n 2 ( 1 ) − 2 ( 2 + 2 t a n 2 ( 1 ) ) t a n ( 1 ) − 2 ( 2 + 2 t a n 2 ( 1 ) ) 1 − ∞ 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a a 2 5 + 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a 2 a 2 3 + 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a a + 2 ( 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a ) a 2 l o g ( − a ) − 2 ( 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a ) a 2 l o g ( a ) − 2 ( 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a ) a 2 l o g ( − a + t a n ( 1 ) ) + 2 ( 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a ) a 2 l o g ( a + t a n ( 1 ) ) + 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a a l o g ( − a ) − 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a a l o g ( a ) − 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a a l o g ( − a + t a n ( 1 ) ) + 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a a l o g ( a + t a n ( 1 ) ) + 2 ( 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a ) l o g ( − a ) − 2 ( 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a ) l o g ( a ) − 2 ( 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a ) l o g ( − a + t a n ( 1 ) ) + 2 ( 2 a 2 7 + 6 a 2 5 + 6 a 2 3 + 2 a ) l o g ( a + t a n ( 1 ) ) for a = − 1 for a = 0 otherwise
Piecewise((-1/(2*(2 + 2*tan(1)^2)) - tan(1)^2/(2*(2 + 2*tan(1)^2)) - tan(1)/(2*(2 + 2*tan(1)^2)), a = -1), (-oo, a = 0), (sqrt(a)/(2*sqrt(a) + 2*a^(7/2) + 6*a^(3/2) + 6*a^(5/2)) + a^(5/2)/(2*sqrt(a) + 2*a^(7/2) + 6*a^(3/2) + 6*a^(5/2)) + log(-sqrt(a))/(2*(2*sqrt(a) + 2*a^(7/2) + 6*a^(3/2) + 6*a^(5/2))) + log(sqrt(a) + tan(1))/(2*(2*sqrt(a) + 2*a^(7/2) + 6*a^(3/2) + 6*a^(5/2))) + 2*a^(3/2)/(2*sqrt(a) + 2*a^(7/2) + 6*a^(3/2) + 6*a^(5/2)) - log(sqrt(a))/(2*(2*sqrt(a) + 2*a^(7/2) + 6*a^(3/2) + 6*a^(5/2))) - log(-sqrt(a) + tan(1))/(2*(2*sqrt(a) + 2*a^(7/2) + 6*a^(3/2) + 6*a^(5/2))) + a*log(-sqrt(a))/(2*sqrt(a) + 2*a^(7/2) + 6*a^(3/2) + 6*a^(5/2)) + a*log(sqrt(a) + tan(1))/(2*sqrt(a) + 2*a^(7/2) + 6*a^(3/2) + 6*a^(5/2)) + a^2*log(-sqrt(a))/(2*(2*sqrt(a) + 2*a^(7/2) + 6*a^(3/2) + 6*a^(5/2))) + a^2*log(sqrt(a) + tan(1))/(2*(2*sqrt(a) + 2*a^(7/2) + 6*a^(3/2) + 6*a^(5/2))) - a*log(sqrt(a))/(2*sqrt(a) + 2*a^(7/2) + 6*a^(3/2) + 6*a^(5/2)) - a*log(-sqrt(a) + tan(1))/(2*sqrt(a) + 2*a^(7/2) + 6*a^(3/2) + 6*a^(5/2)) - a^2*log(sqrt(a))/(2*(2*sqrt(a) + 2*a^(7/2) + 6*a^(3/2) + 6*a^(5/2))) - a^2*log(-sqrt(a) + tan(1))/(2*(2*sqrt(a) + 2*a^(7/2) + 6*a^(3/2) + 6*a^(5/2))), True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.