Sr Examen
Integral de dx/(x*(1+(lnx^2))) dx
Solución
Ha introducido
[src]
x e / | | 1 | --------------- dx | / 2 \ | x*\1 + log (x)/ | / 1
$$\int\limits_{1}^{e^{x}} \frac{1}{x \left(\log{\left(x \right)}^{2} + 1\right)}\, dx$$
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)/ | /
$$\int \frac{1}{x \left(\log{\left(x \right)}^{2} + 1\right)}\, dx = C + \operatorname{RootSum} {\left(4 z^{2} + 1, \left( i \mapsto i \log{\left(2 i + \log{\left(x \right)} \right)} \right)\right)}$$
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 ///
$$- \operatorname{RootSum} {\left(4 z^{2} + 1, \left( i \mapsto i \log{\left(2 i \right)} \right)\right)} + \operatorname{RootSum} {\left(4 z^{2} + 1, \left( i \mapsto i \log{\left(2 i + \log{\left(e^{x} \right)} \right)} \right)\right)}$$
=
=
/ 2 \ / 2 / / x\\\ - RootSum\4*z + 1, i -> i*log(2*i)/ + RootSum\4*z + 1, i -> i*log\2*i + log\e ///
$$- \operatorname{RootSum} {\left(4 z^{2} + 1, \left( i \mapsto i \log{\left(2 i \right)} \right)\right)} + \operatorname{RootSum} {\left(4 z^{2} + 1, \left( i \mapsto i \log{\left(2 i + \log{\left(e^{x} \right)} \right)} \right)\right)}$$
-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.