1 / | | 1 | -------- dx | 2 | 7*x + 8 | / 0
Integral(1/(7*x^2 + 8), (x, 0, 1))
/ | | 1 | -------- dx | 2 | 7*x + 8 | /
1 1 -------- = --------------------- 2 / 2 \ 7*x + 8 |/ ____ \ | ||-\/ 14 | | 8*||--------*x| + 1| \\ 4 / /
/ | | 1 | -------- dx | 2 = | 7*x + 8 | /
/ | | 1 | ----------------- dx | 2 | / ____ \ | |-\/ 14 | | |--------*x| + 1 | \ 4 / | / ----------------------- 8
/ | | 1 | ----------------- dx | 2 | / ____ \ | |-\/ 14 | | |--------*x| + 1 | \ 4 / | / ----------------------- 8
____ -x*\/ 14 v = ---------- 4
/ | | 1 | ------ dv | 2 | 1 + v | / atan(v) ------------ = ------- 8 8
/ | | 1 | ----------------- dx | 2 | / ____ \ | |-\/ 14 | | |--------*x| + 1 / ____\ | \ 4 / ____ |x*\/ 14 | | \/ 14 *atan|--------| / \ 4 / ----------------------- = --------------------- 8 28
/ ____\ ____ |x*\/ 14 | \/ 14 *atan|--------| \ 4 / C + --------------------- 28
/ ____\ / ____ |x*\/ 14 | | \/ 14 *atan|--------| | 1 \ 4 / | -------- dx = C + --------------------- | 2 28 | 7*x + 8 | /
/ ____\ ____ |\/ 14 | \/ 14 *atan|------| \ 4 / ------------------- 28
=
/ ____\ ____ |\/ 14 | \/ 14 *atan|------| \ 4 / ------------------- 28
sqrt(14)*atan(sqrt(14)/4)/28
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.