1 / | | x + 4 | -------------- dx | 2 | 2*x - 6*x + 8 | / 0
Integral((x + 4)/(2*x^2 - 6*x + 8), (x, 0, 1))
/ | | x + 4 | -------------- dx | 2 | 2*x - 6*x + 8 | /
/ 2*2*x - 6 \ |--------------| / 11 \ | 2 | |-----| x + 4 \2*x - 6*x + 8/ \2*7/2/ -------------- = ---------------- + --------------------------- 2 4 2 2*x - 6*x + 8 / ___ ___\ |-2*\/ 7 3*\/ 7 | |--------*x + -------| + 1 \ 7 7 /
/ | | x + 4 | -------------- dx | 2 = | 2*x - 6*x + 8 | /
/ | | 1 / 11* | --------------------------- dx | | 2 | 2*2*x - 6 | / ___ ___\ | -------------- dx | |-2*\/ 7 3*\/ 7 | | 2 | |--------*x + -------| + 1 | 2*x - 6*x + 8 | \ 7 7 / | | / / -------------------- + ------------------------------------ 4 7
/ | | 2*2*x - 6 | -------------- dx | 2 | 2*x - 6*x + 8 | / -------------------- 4
2 u = -6*x + 2*x
/ | | 1 | ----- du | 8 + u | / log(8 + u) ----------- = ---------- 4 4
/ | | 2*2*x - 6 | -------------- dx | 2 | 2*x - 6*x + 8 | / 2 \ / log\4 + x - 3*x/ -------------------- = ----------------- 4 4
/ | | 1 11* | --------------------------- dx | 2 | / ___ ___\ | |-2*\/ 7 3*\/ 7 | | |--------*x + -------| + 1 | \ 7 7 / | / ------------------------------------ 7
___ ___ 3*\/ 7 2*x*\/ 7 v = ------- - --------- 7 7
/ | | 1 11* | ------ dv | 2 | 1 + v | / 11*atan(v) --------------- = ---------- 7 7
/ | | 1 11* | --------------------------- dx | 2 | / ___ ___\ | |-2*\/ 7 3*\/ 7 | | |--------*x + -------| + 1 / ___ ___\ | \ 7 7 / ___ | 3*\/ 7 2*x*\/ 7 | | 11*\/ 7 *atan|- ------- + ---------| / \ 7 7 / ------------------------------------ = ------------------------------------ 7 14
/ ___ ___\ ___ | 3*\/ 7 2*x*\/ 7 | / 2 \ 11*\/ 7 *atan|- ------- + ---------| log\4 + x - 3*x/ \ 7 7 / C + ----------------- + ------------------------------------ 4 14
/ ___ \ / ___ |2*\/ 7 *(-3/2 + x)| | / 2 \ 11*\/ 7 *atan|------------------| | x + 4 log\4 + x - 3*x/ \ 7 / | -------------- dx = C + ----------------- + --------------------------------- | 2 4 14 | 2*x - 6*x + 8 | /
/ ___\ / ___\ ___ |\/ 7 | ___ |3*\/ 7 | 11*\/ 7 *atan|-----| 11*\/ 7 *atan|-------| log(4) log(2) \ 7 / \ 7 / - ------ + ------ - -------------------- + ---------------------- 4 4 14 14
=
/ ___\ / ___\ ___ |\/ 7 | ___ |3*\/ 7 | 11*\/ 7 *atan|-----| 11*\/ 7 *atan|-------| log(4) log(2) \ 7 / \ 7 / - ------ + ------ - -------------------- + ---------------------- 4 4 14 14
-log(4)/4 + log(2)/4 - 11*sqrt(7)*atan(sqrt(7)/7)/14 + 11*sqrt(7)*atan(3*sqrt(7)/7)/14
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.