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Resolución de integrales/ lnx^2/ dx/(x*(1+(lnx^2)))

Integral de dx/(x*(1+(lnx^2))) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  x                   
 e                    
  /                   
 |                    
 |         1          
 |  --------------- dx
 |    /       2   \   
 |  x*\1 + log (x)/   
 |                    
/                     
1
∫1ex1x(log⁡(x)2+1) dx\int\limits_{1}^{e^{x}} \frac{1}{x \left(\log{\left(x \right)}^{2} + 1\right)}\, dx 
Integral(1/(x*(1 + log(x)^2)), (x, 1, exp(x)))
Respuesta (Indefinida) [src] 
  /                                                                    
 |                                                                     
 |        1                        /   2                              \
 | --------------- dx = C + RootSum\4*z  + 1, i -> i*log(2*i + log(x))/
 |   /       2   \                                                     
 | x*\1 + log (x)/                                                     
 |                                                                     
/
∫1x(log⁡(x)2+1) dx=C+RootSum⁡(4z2+1,(i↦ilog⁡(2i+log⁡(x))))\int \frac{1}{x \left(\log{\left(x \right)}^{2} + 1\right)}\, dx = C + \operatorname{RootSum} {\left(4 z^{2} + 1, \left( i \mapsto i \log{\left(2 i + \log{\left(x \right)} \right)} \right)\right)}
Simplificar
Respuesta [src] 
         /   2                     \          /   2                /         / x\\\
- RootSum\4*z  + 1, i -> i*log(2*i)/ + RootSum\4*z  + 1, i -> i*log\2*i + log\e ///
−RootSum⁡(4z2+1,(i↦ilog⁡(2i)))+RootSum⁡(4z2+1,(i↦ilog⁡(2i+log⁡(ex))))- \operatorname{RootSum} {\left(4 z^{2} + 1, \left( i \mapsto i \log{\left(2 i \right)} \right)\right)} + \operatorname{RootSum} {\left(4 z^{2} + 1, \left( i \mapsto i \log{\left(2 i + \log{\left(e^{x} \right)} \right)} \right)\right)} 
=
= 
         /   2                     \          /   2                /         / x\\\
- RootSum\4*z  + 1, i -> i*log(2*i)/ + RootSum\4*z  + 1, i -> i*log\2*i + log\e ///
−RootSum⁡(4z2+1,(i↦ilog⁡(2i)))+RootSum⁡(4z2+1,(i↦ilog⁡(2i+log⁡(ex))))- \operatorname{RootSum} {\left(4 z^{2} + 1, \left( i \mapsto i \log{\left(2 i \right)} \right)\right)} + \operatorname{RootSum} {\left(4 z^{2} + 1, \left( i \mapsto i \log{\left(2 i + \log{\left(e^{x} \right)} \right)} \right)\right)} 
-RootSum(4*_z^2 + 1, Lambda(_i, _i*log(2*_i))) + RootSum(4*_z^2 + 1, Lambda(_i, _i*log(2*_i + log(exp(x)))))

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

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