1 / | | 2*x + 1 | ------------ dx | 2 | x + 4*x + 5 | / 0
Integral((2*x + 1)/(x^2 + 4*x + 5), (x, 0, 1))
/ | | 2*x + 1 | ------------ dx | 2 | x + 4*x + 5 | /
/-3 \ |---| 2*x + 1 2*x + 4 \ 1 / ------------ = ------------ + ------------- 2 2 2 x + 4*x + 5 x + 4*x + 5 (-x - 2) + 1
/ | | 2*x + 1 | ------------ dx | 2 = | x + 4*x + 5 | /
/ / | | | 1 | 2*x + 4 - 3* | ------------- dx + | ------------ dx | 2 | 2 | (-x - 2) + 1 | x + 4*x + 5 | | / /
/ | | 2*x + 4 | ------------ dx | 2 | x + 4*x + 5 | /
2 u = x + 4*x
/ | | 1 | ----- du = log(5 + u) | 5 + u | /
/ | | 2*x + 4 / 2 \ | ------------ dx = log\5 + x + 4*x/ | 2 | x + 4*x + 5 | /
/ | | 1 -3* | ------------- dx | 2 | (-x - 2) + 1 | /
v = -2 - x
/ | | 1 -3* | ------ dv = -3*atan(v) | 2 | 1 + v | /
/ | | 1 -3* | ------------- dx = -3*atan(2 + x) | 2 | (-x - 2) + 1 | /
/ 2 \ C - 3*atan(2 + x) + log\5 + x + 4*x/
/ | | 2*x + 1 / 2 \ | ------------ dx = C - 3*atan(2 + x) + log\5 + x + 4*x/ | 2 | x + 4*x + 5 | /
-log(5) - 3*atan(3) + 3*atan(2) + log(10)
=
-log(5) - 3*atan(3) + 3*atan(2) + log(10)
-log(5) - 3*atan(3) + 3*atan(2) + log(10)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.