1 / | | 2*x | ------------ dx | 2 | x + 2*x + 2 | / 0
Integral((2*x)/(x^2 + 2*x + 2), (x, 0, 1))
/ | | 2*x | ------------ dx | 2 | x + 2*x + 2 | /
/-2 \ |---| 2*x 2*x + 2 \ 1 / ------------ = ------------ + ------------- 2 2 2 x + 2*x + 2 x + 2*x + 2 (-x - 1) + 1
/ | | 2*x | ------------ dx | 2 = | x + 2*x + 2 | /
/ / | | | 1 | 2*x + 2 - 2* | ------------- dx + | ------------ dx | 2 | 2 | (-x - 1) + 1 | x + 2*x + 2 | | / /
/ | | 2*x + 2 | ------------ dx | 2 | x + 2*x + 2 | /
2 u = x + 2*x
/ | | 1 | ----- du = log(2 + u) | 2 + u | /
/ | | 2*x + 2 / 2 \ | ------------ dx = log\2 + x + 2*x/ | 2 | x + 2*x + 2 | /
/ | | 1 -2* | ------------- dx | 2 | (-x - 1) + 1 | /
v = -1 - x
/ | | 1 -2* | ------ dv = -2*atan(v) | 2 | 1 + v | /
/ | | 1 -2* | ------------- dx = -2*atan(1 + x) | 2 | (-x - 1) + 1 | /
/ 2 \ C - 2*atan(1 + x) + log\2 + x + 2*x/
/ | | 2*x / 2 \ | ------------ dx = C - 2*atan(1 + x) + log\2 + x + 2*x/ | 2 | x + 2*x + 2 | /
pi -- - log(2) - 2*atan(2) + log(5) 2
=
pi -- - log(2) - 2*atan(2) + log(5) 2
pi/2 - log(2) - 2*atan(2) + log(5)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.