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