oo / | | x | ------------ dx | 2 | x + 4*x + 7 | / -1
Integral(x/(x^2 + 4*x + 7), (x, -1, oo))
/ | | x | ------------ dx | 2 | x + 4*x + 7 | /
/ 2*x + 4 \ |------------| /-2 \ | 2 | |---| x \x + 4*x + 7/ \ 3 / ------------ = -------------- + -------------------------- 2 2 2 x + 4*x + 7 / ___ ___\ |-\/ 3 2*\/ 3 | |-------*x - -------| + 1 \ 3 3 /
/ | | x | ------------ dx | 2 = | x + 4*x + 7 | /
/ | | 1 / 2* | -------------------------- dx | | 2 | 2*x + 4 | / ___ ___\ | ------------ dx | |-\/ 3 2*\/ 3 | | 2 | |-------*x - -------| + 1 | x + 4*x + 7 | \ 3 3 / | | / / ------------------ - ---------------------------------- 2 3
/ | | 2*x + 4 | ------------ dx | 2 | x + 4*x + 7 | / ------------------ 2
2 u = x + 4*x
/ | | 1 | ----- du | 7 + u | / log(7 + u) ----------- = ---------- 2 2
/ | | 2*x + 4 | ------------ dx | 2 | x + 4*x + 7 | / 2 \ / log\7 + x + 4*x/ ------------------ = ----------------- 2 2
/ | | 1 -2* | -------------------------- dx | 2 | / ___ ___\ | |-\/ 3 2*\/ 3 | | |-------*x - -------| + 1 | \ 3 3 / | / ----------------------------------- 3
___ ___ 2*\/ 3 x*\/ 3 v = - ------- - ------- 3 3
/ | | 1 -2* | ------ dv | 2 | 1 + v | / -2*atan(v) --------------- = ---------- 3 3
/ | | 1 -2* | -------------------------- dx | 2 | / ___ ___\ | |-\/ 3 2*\/ 3 | | |-------*x - -------| + 1 / ___ ___\ | \ 3 3 / ___ |2*\/ 3 x*\/ 3 | | -2*\/ 3 *atan|------- + -------| / \ 3 3 / ----------------------------------- = -------------------------------- 3 3
/ ___ ___\ ___ |2*\/ 3 x*\/ 3 | / 2 \ 2*\/ 3 *atan|------- + -------| log\7 + x + 4*x/ \ 3 3 / C + ----------------- - ------------------------------- 2 3
/ ___ \ / ___ |\/ 3 *(2 + x)| | / 2 \ 2*\/ 3 *atan|-------------| | x log\7 + x + 4*x/ \ 3 / | ------------ dx = C + ----------------- - --------------------------- | 2 2 3 | x + 4*x + 7 | /
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.