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