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