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