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

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
  E                   
  /                   
 |                    
 |         1          
 |  --------------- dx
 |    /       2   \   
 |  x*\1 + log (x)/   
 |                    
/                     
1                     
1e1x(log(x)2+1)dx\int\limits_{1}^{e} \frac{1}{x \left(\log{\left(x \right)}^{2} + 1\right)}\, dx
Integral(1/(x*(1 + log(x)^2)), (x, 1, E))
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,(iilog(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)}
Gráfica
1.01.21.41.61.82.02.22.42.62.5-2.5
Respuesta [src]
         /   2                     \          /   2                         \
- RootSum\4*z  + 1, i -> i*log(2*i)/ + RootSum\4*z  + 1, i -> i*log(1 + 2*i)/
RootSum(4z2+1,(iilog(2i)))+RootSum(4z2+1,(iilog(2i+1)))- \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 + 1 \right)} \right)\right)}
=
=
         /   2                     \          /   2                         \
- RootSum\4*z  + 1, i -> i*log(2*i)/ + RootSum\4*z  + 1, i -> i*log(1 + 2*i)/
RootSum(4z2+1,(iilog(2i)))+RootSum(4z2+1,(iilog(2i+1)))- \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 + 1 \right)} \right)\right)}
-RootSum(4*_z^2 + 1, Lambda(_i, _i*log(2*_i))) + RootSum(4*_z^2 + 1, Lambda(_i, _i*log(1 + 2*_i)))
Respuesta numérica [src]
0.785398163397448
0.785398163397448

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