oo / | | 1 | ------------- dx | 2 | x + 4*x + 12 | / 0
Integral(1/(x^2 + 4*x + 12), (x, 0, oo))
/ | | 1 | ------------- dx | 2 | x + 4*x + 12 | /
1 1 ------------- = ---------------------------- 2 / 2 \ x + 4*x + 12 |/ ___ ___\ | ||-\/ 2 \/ 2 | | 8*||-------*x - -----| + 1| \\ 4 2 / /
/ | | 1 | ------------- dx | 2 = | x + 4*x + 12 | /
/ | | 1 | ------------------------ dx | 2 | / ___ ___\ | |-\/ 2 \/ 2 | | |-------*x - -----| + 1 | \ 4 2 / | / ------------------------------ 8
/ | | 1 | ------------------------ dx | 2 | / ___ ___\ | |-\/ 2 \/ 2 | | |-------*x - -----| + 1 | \ 4 2 / | / ------------------------------ 8
___ ___ \/ 2 x*\/ 2 v = - ----- - ------- 2 4
/ | | 1 | ------ dv | 2 | 1 + v | / atan(v) ------------ = ------- 8 8
/ | | 1 | ------------------------ dx | 2 | / ___ ___\ | |-\/ 2 \/ 2 | | |-------*x - -----| + 1 / ___ ___\ | \ 4 2 / ___ |\/ 2 x*\/ 2 | | \/ 2 *atan|----- + -------| / \ 2 4 / ------------------------------ = --------------------------- 8 4
/ ___ ___\ ___ |\/ 2 x*\/ 2 | \/ 2 *atan|----- + -------| \ 2 4 / C + --------------------------- 4
/ ___ \ / ___ |\/ 2 *(2 + x)| | \/ 2 *atan|-------------| | 1 \ 4 / | ------------- dx = C + ------------------------- | 2 4 | x + 4*x + 12 | /
/ ___\ ___ |\/ 2 | \/ 2 *atan|-----| ___ \ 2 / pi*\/ 2 - ----------------- + -------- 4 8
=
/ ___\ ___ |\/ 2 | \/ 2 *atan|-----| ___ \ 2 / pi*\/ 2 - ----------------- + -------- 4 8
-sqrt(2)*atan(sqrt(2)/2)/4 + pi*sqrt(2)/8
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.