1 / | | 1 | -------- dx | 2 | 5*x + 3 | / 0
Integral(1/(5*x^2 + 3), (x, 0, 1))
/ | | 1 | -------- dx | 2 | 5*x + 3 | /
1 1 -------- = --------------------- 2 / 2 \ 5*x + 3 |/ ____ \ | ||-\/ 15 | | 3*||--------*x| + 1| \\ 3 / /
/ | | 1 | -------- dx | 2 = | 5*x + 3 | /
/ | | 1 | ----------------- dx | 2 | / ____ \ | |-\/ 15 | | |--------*x| + 1 | \ 3 / | / ----------------------- 3
/ | | 1 | ----------------- dx | 2 | / ____ \ | |-\/ 15 | | |--------*x| + 1 | \ 3 / | / ----------------------- 3
____ -x*\/ 15 v = ---------- 3
/ | | 1 | ------ dv | 2 | 1 + v | / atan(v) ------------ = ------- 3 3
/ | | 1 | ----------------- dx | 2 | / ____ \ | |-\/ 15 | | |--------*x| + 1 / ____\ | \ 3 / ____ |x*\/ 15 | | \/ 15 *atan|--------| / \ 3 / ----------------------- = --------------------- 3 15
/ ____\ ____ |x*\/ 15 | \/ 15 *atan|--------| \ 3 / C + --------------------- 15
/ ____\ / ____ |x*\/ 15 | | \/ 15 *atan|--------| | 1 \ 3 / | -------- dx = C + --------------------- | 2 15 | 5*x + 3 | /
/ ____\ ____ |\/ 15 | \/ 15 *atan|------| \ 3 / ------------------- 15
=
/ ____\ ____ |\/ 15 | \/ 15 *atan|------| \ 3 / ------------------- 15
sqrt(15)*atan(sqrt(15)/3)/15
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.