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Resolución de integrales/ (1/3)/ 2+x^2/ sin(1/3)*ln(0.2+x^2)

Integral de sin(1/3)*ln(0.2+x^2) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  3                        
  /                        
 |                         
 |              /1    2\   
 |  sin(1/3)*log|- + x | dx
 |              \5     /   
 |                         
/                          
1
$$\int\limits_{1}^{3} \log{\left(x^{2} + \frac{1}{5} \right)} \sin{\left(\frac{1}{3} \right)}\, dx$$ 
Integral(sin(1/3)*log(1/5 + x^2), (x, 1, 3))
Respuesta (Indefinida) [src] 
  /                                                                                     
 |                               /                           ___     /    ___\\         
 |             /1    2\          |            /1    2\   2*\/ 5 *atan\x*\/ 5 /|         
 | sin(1/3)*log|- + x | dx = C + |-2*x + x*log|- + x | + ---------------------|*sin(1/3)
 |             \5     /          \            \5     /             5          /         
 |                                                                                      
/
$$\int \log{\left(x^{2} + \frac{1}{5} \right)} \sin{\left(\frac{1}{3} \right)}\, dx = C + \left(x \log{\left(x^{2} + \frac{1}{5} \right)} - 2 x + \frac{2 \sqrt{5} \operatorname{atan}{\left(\sqrt{5} x \right)}}{5}\right) \sin{\left(\frac{1}{3} \right)}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
                        /      ___     /    ___\\                                      /      ___     /  ___\\         
                        |3   \/ 5 *atan\3*\/ 5 /|                                      |1   \/ 5 *atan\\/ 5 /|         
-log(6/5)*sin(1/3) - 10*|- - -------------------|*sin(1/3) + 3*log(46/5)*sin(1/3) + 10*|- - -----------------|*sin(1/3)
                        \5            25        /                                      \5           25       /
$$- 10 \left(- \frac{\sqrt{5} \operatorname{atan}{\left(3 \sqrt{5} \right)}}{25} + \frac{3}{5}\right) \sin{\left(\frac{1}{3} \right)} - \log{\left(\frac{6}{5} \right)} \sin{\left(\frac{1}{3} \right)} + 10 \left(- \frac{\sqrt{5} \operatorname{atan}{\left(\sqrt{5} \right)}}{25} + \frac{1}{5}\right) \sin{\left(\frac{1}{3} \right)} + 3 \log{\left(\frac{46}{5} \right)} \sin{\left(\frac{1}{3} \right)}$$ 
=
= 
                        /      ___     /    ___\\                                      /      ___     /  ___\\         
                        |3   \/ 5 *atan\3*\/ 5 /|                                      |1   \/ 5 *atan\\/ 5 /|         
-log(6/5)*sin(1/3) - 10*|- - -------------------|*sin(1/3) + 3*log(46/5)*sin(1/3) + 10*|- - -----------------|*sin(1/3)
                        \5            25        /                                      \5           25       /
$$- 10 \left(- \frac{\sqrt{5} \operatorname{atan}{\left(3 \sqrt{5} \right)}}{25} + \frac{3}{5}\right) \sin{\left(\frac{1}{3} \right)} - \log{\left(\frac{6}{5} \right)} \sin{\left(\frac{1}{3} \right)} + 10 \left(- \frac{\sqrt{5} \operatorname{atan}{\left(\sqrt{5} \right)}}{25} + \frac{1}{5}\right) \sin{\left(\frac{1}{3} \right)} + 3 \log{\left(\frac{46}{5} \right)} \sin{\left(\frac{1}{3} \right)}$$ 
-log(6/5)*sin(1/3) - 10*(3/5 - sqrt(5)*atan(3*sqrt(5))/25)*sin(1/3) + 3*log(46/5)*sin(1/3) + 10*(1/5 - sqrt(5)*atan(sqrt(5))/25)*sin(1/3)
Respuesta numérica [src] 
0.889664498080062
0.889664498080062

    Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.

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