Sr Examen
Integral de (arctgxdx)/(1+x)^2 dx
Solución
Ha introducido
[src]
1 / | | acot(x) | -------- dx | 2 | (1 + x) | / 0
$$\int\limits_{0}^{1} \frac{\operatorname{acot}{\left(x \right)}}{\left(x + 1\right)^{2}}\, dx$$
Integral(acot(x)/(1 + x)^2, (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | / 2\ / 2\ | acot(x) log\1 + x / 2*acot(x) 2*log(1 + x) x*log\1 + x / 2*x*log(1 + x) 2*x*acot(x) | -------- dx = C + ----------- - --------- - ------------ + ------------- - -------------- + ----------- | 2 4 + 4*x 4 + 4*x 4 + 4*x 4 + 4*x 4 + 4*x 4 + 4*x | (1 + x) | /
$$\int \frac{\operatorname{acot}{\left(x \right)}}{\left(x + 1\right)^{2}}\, dx = C - \frac{2 x \log{\left(x + 1 \right)}}{4 x + 4} + \frac{x \log{\left(x^{2} + 1 \right)}}{4 x + 4} + \frac{2 x \operatorname{acot}{\left(x \right)}}{4 x + 4} - \frac{2 \log{\left(x + 1 \right)}}{4 x + 4} + \frac{\log{\left(x^{2} + 1 \right)}}{4 x + 4} - \frac{2 \operatorname{acot}{\left(x \right)}}{4 x + 4}$$
Gráfica
Respuesta
[src]
log(2) pi
- ------ + --
4 4
$$- \frac{\log{\left(2 \right)}}{4} + \frac{\pi}{4}$$
=
=
log(2) pi
- ------ + --
4 4
$$- \frac{\log{\left(2 \right)}}{4} + \frac{\pi}{4}$$
-log(2)/4 + pi/4
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.