1 / | | 1 | ------ dx | 2 | 7 + x | / 0
Integral(1/(7 + x^2), (x, 0, 1))
/ | | 1 | ------ dx | 2 | 7 + x | /
1 1 ------ = -------------------- 2 / 2 \ 7 + x |/ ___ \ | ||-\/ 7 | | 7*||-------*x| + 1| \\ 7 / /
/ | | 1 | ------ dx | 2 = | 7 + x | /
/ | | 1 | ---------------- dx | 2 | / ___ \ | |-\/ 7 | | |-------*x| + 1 | \ 7 / | / ---------------------- 7
/ | | 1 | ---------------- dx | 2 | / ___ \ | |-\/ 7 | | |-------*x| + 1 | \ 7 / | / ---------------------- 7
___ -x*\/ 7 v = --------- 7
/ | | 1 | ------ dv | 2 | 1 + v | / atan(v) ------------ = ------- 7 7
/ | | 1 | ---------------- dx | 2 | / ___ \ | |-\/ 7 | | |-------*x| + 1 / ___\ | \ 7 / ___ |x*\/ 7 | | \/ 7 *atan|-------| / \ 7 / ---------------------- = ------------------- 7 7
/ ___\ ___ |x*\/ 7 | \/ 7 *atan|-------| \ 7 / C + ------------------- 7
/ ___\ / ___ |x*\/ 7 | | \/ 7 *atan|-------| | 1 \ 7 / | ------ dx = C + ------------------- | 2 7 | 7 + x | /
/ ___\ ___ |\/ 7 | \/ 7 *atan|-----| \ 7 / ----------------- 7
=
/ ___\ ___ |\/ 7 | \/ 7 *atan|-----| \ 7 / ----------------- 7
sqrt(7)*atan(sqrt(7)/7)/7
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.