1 / | | 2*x + 3 | ------------ dx | 2 | x + 3*x + 4 | / 0
Integral((2*x + 3)/(x^2 + 3*x + 4), (x, 0, 1))
/ | | 2*x + 3 | ------------ dx | 2 | x + 3*x + 4 | /
/ 0 \ |---| 2*x + 3 2*x + 3 \7/4/ ------------ = ------------ + --------------------------- 2 2 2 x + 3*x + 4 x + 3*x + 4 / ___ ___\ |-2*\/ 7 3*\/ 7 | |--------*x - -------| + 1 \ 7 7 /
/ | | 2*x + 3 | ------------ dx | 2 = | x + 3*x + 4 | /
/ | | 2*x + 3 | ------------ dx | 2 | x + 3*x + 4 | /
/ | | 2*x + 3 | ------------ dx | 2 | x + 3*x + 4 | /
2 u = x + 3*x
/ | | 1 | ----- du = log(4 + u) | 4 + u | /
/ | | 2*x + 3 / 2 \ | ------------ dx = log\4 + x + 3*x/ | 2 | x + 3*x + 4 | /
0
___ ___ 3*\/ 7 2*x*\/ 7 v = - ------- - --------- 7 7
True
True
/ 2 \ C + log\4 + x + 3*x/
/ | | 2*x + 3 / 2 \ | ------------ dx = C + log\x + 3*x + 4/ | 2 | x + 3*x + 4 | /
-log(4) + log(8)
=
-log(4) + log(8)
-log(4) + log(8)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.