Sr Examen
Integral de (x^a/((e^x)-1))sin1/x dx
Solución
Ha introducido
[src]
1 / | | a | x | ------*sin(1) | x | E - 1 | ------------- dx | x | / 0
$$\int\limits_{0}^{1} \frac{\frac{x^{a}}{e^{x} - 1} \sin{\left(1 \right)}}{x}\, dx$$
Integral(((x^a/(E^x - 1))*sin(1))/x, (x, 0, 1))
Respuesta (Indefinida)
[src]
/
|
| a
| x / / \
| ------*sin(1) | | |
| x | | a |
| E - 1 | | x |
| ------------- dx = C + | | ----------- dx|*sin(1)
| x | | / x\ |
| | | x*\-1 + e / |
/ | | |
\/ /
$$\int \frac{\frac{x^{a}}{e^{x} - 1} \sin{\left(1 \right)}}{x}\, dx = C + \sin{\left(1 \right)} \int \frac{x^{a}}{x \left(e^{x} - 1\right)}\, dx$$
Respuesta
[src]
/ 1 \ | / | | | | | | a | | | x | | | --------- dx|*sin(1) | | x | | | -x + x*e | | | | |/ | \0 /
$$\sin{\left(1 \right)} \int\limits_{0}^{1} \frac{x^{a}}{x e^{x} - x}\, dx$$
=
=
/ 1 \ | / | | | | | | a | | | x | | | --------- dx|*sin(1) | | x | | | -x + x*e | | | | |/ | \0 /
$$\sin{\left(1 \right)} \int\limits_{0}^{1} \frac{x^{a}}{x e^{x} - x}\, dx$$
Integral(x^a/(-x + x*exp(x)), (x, 0, 1))*sin(1)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.