Sr Examen
Integral de 1/(x*log(x+1)^2) dx
Solución
Ha introducido
[src]
oo / | | 1 | ------------- dx | 2 | x*log (x + 1) | / 1
$$\int\limits_{1}^{\infty} \frac{1}{x \log{\left(x + 1 \right)}^{2}}\, dx$$
Integral(1/(x*log(x + 1)^2), (x, 1, oo))
Respuesta (Indefinida)
[src]
/ / | | | 1 | 1 -1 - x | ------------- dx = C - | ------------- dx + ------------ | 2 | 2 x*log(1 + x) | x*log (x + 1) | x *log(1 + x) | | / /
$$\int \frac{1}{x \log{\left(x + 1 \right)}^{2}}\, dx = C - \int \frac{1}{x^{2} \log{\left(x + 1 \right)}}\, dx + \frac{- x - 1}{x \log{\left(x + 1 \right)}}$$
Respuesta
[src]
oo
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| 1 2
- | ------------- dx + ------
| 2 log(2)
| x *log(1 + x)
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1
$$- \int\limits_{1}^{\infty} \frac{1}{x^{2} \log{\left(x + 1 \right)}}\, dx + \frac{2}{\log{\left(2 \right)}}$$
=
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oo
/
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| 1 2
- | ------------- dx + ------
| 2 log(2)
| x *log(1 + x)
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/
1
$$- \int\limits_{1}^{\infty} \frac{1}{x^{2} \log{\left(x + 1 \right)}}\, dx + \frac{2}{\log{\left(2 \right)}}$$
-Integral(1/(x^2*log(1 + x)), (x, 1, oo)) + 2/log(2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.