1 / | | x - 4 | ------------ dx | 2 | x - 3*x + 4 | / 0
Integral((x - 4)/(x^2 - 3*x + 4), (x, 0, 1))
/ | | x - 4 | ------------ dx | 2 | x - 3*x + 4 | /
/ 2*x - 3 \ |------------| / -5 \ | 2 | |-----| x - 4 \x - 3*x + 4/ \2*7/4/ ------------ = -------------- + --------------------------- 2 2 2 x - 3*x + 4 / ___ ___\ |-2*\/ 7 3*\/ 7 | |--------*x + -------| + 1 \ 7 7 /
/ | | x - 4 | ------------ dx | 2 = | x - 3*x + 4 | /
/ | | 1 / 10* | --------------------------- dx | | 2 | 2*x - 3 | / ___ ___\ | ------------ dx | |-2*\/ 7 3*\/ 7 | | 2 | |--------*x + -------| + 1 | x - 3*x + 4 | \ 7 7 / | | / / ------------------ - ------------------------------------ 2 7
/ | | 2*x - 3 | ------------ dx | 2 | x - 3*x + 4 | / ------------------ 2
2 u = x - 3*x
/ | | 1 | ----- du | 4 + u | / log(4 + u) ----------- = ---------- 2 2
/ | | 2*x - 3 | ------------ dx | 2 | x - 3*x + 4 | / 2 \ / log\4 + x - 3*x/ ------------------ = ----------------- 2 2
/ | | 1 -10* | --------------------------- dx | 2 | / ___ ___\ | |-2*\/ 7 3*\/ 7 | | |--------*x + -------| + 1 | \ 7 7 / | / ------------------------------------- 7
___ ___ 3*\/ 7 2*x*\/ 7 v = ------- - --------- 7 7
/ | | 1 -10* | ------ dv | 2 | 1 + v | / -10*atan(v) ---------------- = ----------- 7 7
/ | | 1 -10* | --------------------------- dx | 2 | / ___ ___\ | |-2*\/ 7 3*\/ 7 | | |--------*x + -------| + 1 / ___ ___\ | \ 7 7 / ___ | 3*\/ 7 2*x*\/ 7 | | -5*\/ 7 *atan|- ------- + ---------| / \ 7 7 / ------------------------------------- = ------------------------------------ 7 7
/ ___ ___\ ___ | 3*\/ 7 2*x*\/ 7 | / 2 \ 5*\/ 7 *atan|- ------- + ---------| log\4 + x - 3*x/ \ 7 7 / C + ----------------- - ----------------------------------- 2 7
/ ___ \ / ___ |2*\/ 7 *(-3/2 + x)| | / 2 \ 5*\/ 7 *atan|------------------| | x - 4 log\4 + x - 3*x/ \ 7 / | ------------ dx = C + ----------------- - -------------------------------- | 2 2 7 | x - 3*x + 4 | /
/ ___\ / ___\ ___ |3*\/ 7 | ___ |\/ 7 | 5*\/ 7 *atan|-------| 5*\/ 7 *atan|-----| log(2) log(4) \ 7 / \ 7 / ------ - ------ - --------------------- + ------------------- 2 2 7 7
=
/ ___\ / ___\ ___ |3*\/ 7 | ___ |\/ 7 | 5*\/ 7 *atan|-------| 5*\/ 7 *atan|-----| log(2) log(4) \ 7 / \ 7 / ------ - ------ - --------------------- + ------------------- 2 2 7 7
log(2)/2 - log(4)/2 - 5*sqrt(7)*atan(3*sqrt(7)/7)/7 + 5*sqrt(7)*atan(sqrt(7)/7)/7
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.