1 / | | 2*x - 5 | ------------ dx | 2 | x - 5*x + 7 | / 0
Integral((2*x - 5)/(x^2 - 5*x + 7), (x, 0, 1))
/ | | 2*x - 5 | ------------ dx | 2 | x - 5*x + 7 | /
/ 0 \ |---| 2*x - 5 2*x - 5 \3/4/ ------------ = ------------ + --------------------------- 2 2 2 x - 5*x + 7 x - 5*x + 7 / ___ ___\ |-2*\/ 3 5*\/ 3 | |--------*x + -------| + 1 \ 3 3 /
/ | | 2*x - 5 | ------------ dx | 2 = | x - 5*x + 7 | /
/ | | 2*x - 5 | ------------ dx | 2 | x - 5*x + 7 | /
/ | | 2*x - 5 | ------------ dx | 2 | x - 5*x + 7 | /
2 u = x - 5*x
/ | | 1 | ----- du = log(7 + u) | 7 + u | /
/ | | 2*x - 5 / 2 \ | ------------ dx = log\7 + x - 5*x/ | 2 | x - 5*x + 7 | /
0
___ ___ 5*\/ 3 2*x*\/ 3 v = ------- - --------- 3 3
True
True
/ 2 \ C + log\7 + x - 5*x/
/ | | 2*x - 5 / 2 \ | ------------ dx = C + log\x - 5*x + 7/ | 2 | x - 5*x + 7 | /
-log(7) + log(3)
=
-log(7) + log(3)
-log(7) + log(3)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.