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