1 / | | 1 | -------- dx | 2 | 3*x + 4 | / 0
Integral(1/(3*x^2 + 4), (x, 0, 1))
/ | | 1 | -------- dx | 2 | 3*x + 4 | /
1 1 -------- = -------------------- 2 / 2 \ 3*x + 4 |/ ___ \ | ||-\/ 3 | | 4*||-------*x| + 1| \\ 2 / /
/ | | 1 | -------- dx | 2 = | 3*x + 4 | /
/ | | 1 | ---------------- dx | 2 | / ___ \ | |-\/ 3 | | |-------*x| + 1 | \ 2 / | / ---------------------- 4
/ | | 1 | ---------------- dx | 2 | / ___ \ | |-\/ 3 | | |-------*x| + 1 | \ 2 / | / ---------------------- 4
___ -x*\/ 3 v = --------- 2
/ | | 1 | ------ dv | 2 | 1 + v | / atan(v) ------------ = ------- 4 4
/ | | 1 | ---------------- dx | 2 | / ___ \ | |-\/ 3 | | |-------*x| + 1 / ___\ | \ 2 / ___ |x*\/ 3 | | \/ 3 *atan|-------| / \ 2 / ---------------------- = ------------------- 4 6
/ ___\ ___ |x*\/ 3 | \/ 3 *atan|-------| \ 2 / C + ------------------- 6
/ ___\ / ___ |x*\/ 3 | | \/ 3 *atan|-------| | 1 \ 2 / | -------- dx = C + ------------------- | 2 6 | 3*x + 4 | /
/ ___\ ___ |\/ 3 | \/ 3 *atan|-----| \ 2 / ----------------- 6
=
/ ___\ ___ |\/ 3 | \/ 3 *atan|-----| \ 2 / ----------------- 6
sqrt(3)*atan(sqrt(3)/2)/6
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.