oo / | | 1 | ------------ dx | 2 | x + 2*x + 7 | / -oo
Integral(1/(x^2 + 2*x + 7), (x, -oo, oo))
/ | | 1 | ------------ dx | 2 | x + 2*x + 7 | /
1 1 ------------ = ---------------------------- 2 / 2 \ x + 2*x + 7 |/ ___ ___\ | ||-\/ 6 \/ 6 | | 6*||-------*x - -----| + 1| \\ 6 6 / /
/ | | 1 | ------------ dx | 2 = | x + 2*x + 7 | /
/ | | 1 | ------------------------ dx | 2 | / ___ ___\ | |-\/ 6 \/ 6 | | |-------*x - -----| + 1 | \ 6 6 / | / ------------------------------ 6
/ | | 1 | ------------------------ dx | 2 | / ___ ___\ | |-\/ 6 \/ 6 | | |-------*x - -----| + 1 | \ 6 6 / | / ------------------------------ 6
___ ___ \/ 6 x*\/ 6 v = - ----- - ------- 6 6
/ | | 1 | ------ dv | 2 | 1 + v | / atan(v) ------------ = ------- 6 6
/ | | 1 | ------------------------ dx | 2 | / ___ ___\ | |-\/ 6 \/ 6 | | |-------*x - -----| + 1 / ___ ___\ | \ 6 6 / ___ |\/ 6 x*\/ 6 | | \/ 6 *atan|----- + -------| / \ 6 6 / ------------------------------ = --------------------------- 6 6
/ ___ ___\ ___ |\/ 6 x*\/ 6 | \/ 6 *atan|----- + -------| \ 6 6 / C + --------------------------- 6
/ ___ \ / ___ |\/ 6 *(1 + x)| | \/ 6 *atan|-------------| | 1 \ 6 / | ------------ dx = C + ------------------------- | 2 6 | x + 2*x + 7 | /
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.