1 / | | 1 | ------ dx | 2 | 5 + x | / 0
Integral(1/(5 + x^2), (x, 0, 1))
/ | | 1 | ------ dx | 2 | 5 + x | /
1 1 ------ = -------------------- 2 / 2 \ 5 + x |/ ___ \ | ||-\/ 5 | | 5*||-------*x| + 1| \\ 5 / /
/ | | 1 | ------ dx | 2 = | 5 + x | /
/ | | 1 | ---------------- dx | 2 | / ___ \ | |-\/ 5 | | |-------*x| + 1 | \ 5 / | / ---------------------- 5
/ | | 1 | ---------------- dx | 2 | / ___ \ | |-\/ 5 | | |-------*x| + 1 | \ 5 / | / ---------------------- 5
___ -x*\/ 5 v = --------- 5
/ | | 1 | ------ dv | 2 | 1 + v | / atan(v) ------------ = ------- 5 5
/ | | 1 | ---------------- dx | 2 | / ___ \ | |-\/ 5 | | |-------*x| + 1 / ___\ | \ 5 / ___ |x*\/ 5 | | \/ 5 *atan|-------| / \ 5 / ---------------------- = ------------------- 5 5
/ ___\ ___ |x*\/ 5 | \/ 5 *atan|-------| \ 5 / C + ------------------- 5
/ ___\ / ___ |x*\/ 5 | | \/ 5 *atan|-------| | 1 \ 5 / | ------ dx = C + ------------------- | 2 5 | 5 + x | /
/ ___\ ___ |\/ 5 | \/ 5 *atan|-----| \ 5 / ----------------- 5
=
/ ___\ ___ |\/ 5 | \/ 5 *atan|-----| \ 5 / ----------------- 5
sqrt(5)*atan(sqrt(5)/5)/5
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.