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