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