1 / | | 1 | ------------ dx | 2 | 6*x - x + 1 | / 0
Integral(1/(6*x^2 - x + 1), (x, 0, 1))
/ | | 1 | ------------ dx | 2 | 6*x - x + 1 | /
1 1 ------------ = --------------------------------- 2 / 2 \ 6*x - x + 1 |/ ____ ____\ | 23 ||-12*\/ 23 \/ 23 | | --*||----------*x + ------| + 1| 24 \\ 23 23 / /
/ | | 1 | ------------ dx | 2 = | 6*x - x + 1 | /
/ | | 1 24* | ---------------------------- dx | 2 | / ____ ____\ | |-12*\/ 23 \/ 23 | | |----------*x + ------| + 1 | \ 23 23 / | / ------------------------------------- 23
/ | | 1 24* | ---------------------------- dx | 2 | / ____ ____\ | |-12*\/ 23 \/ 23 | | |----------*x + ------| + 1 | \ 23 23 / | / ------------------------------------- 23
____ ____ \/ 23 12*x*\/ 23 v = ------ - ----------- 23 23
/ | | 1 24* | ------ dv | 2 | 1 + v | / 24*atan(v) --------------- = ---------- 23 23
/ | | 1 24* | ---------------------------- dx | 2 | / ____ ____\ | |-12*\/ 23 \/ 23 | | |----------*x + ------| + 1 / ____ ____\ | \ 23 23 / ____ | \/ 23 12*x*\/ 23 | | 2*\/ 23 *atan|- ------ + -----------| / \ 23 23 / ------------------------------------- = ------------------------------------- 23 23
/ ____ ____\ ____ | \/ 23 12*x*\/ 23 | 2*\/ 23 *atan|- ------ + -----------| \ 23 23 / C + ------------------------------------- 23
/ ____ \ / ____ |12*\/ 23 *(-1/12 + x)| | 2*\/ 23 *atan|---------------------| | 1 \ 23 / | ------------ dx = C + ------------------------------------ | 2 23 | 6*x - x + 1 | /
/ ____\ / ____\ ____ |\/ 23 | ____ |11*\/ 23 | 2*\/ 23 *atan|------| 2*\/ 23 *atan|---------| \ 23 / \ 23 / --------------------- + ------------------------ 23 23
=
/ ____\ / ____\ ____ |\/ 23 | ____ |11*\/ 23 | 2*\/ 23 *atan|------| 2*\/ 23 *atan|---------| \ 23 / \ 23 / --------------------- + ------------------------ 23 23
2*sqrt(23)*atan(sqrt(23)/23)/23 + 2*sqrt(23)*atan(11*sqrt(23)/23)/23
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.