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