1 / | | 1 | -------------- dx | 2 | x - 10*x + 29 | / 0
Integral(1/(x^2 - 10*x + 29), (x, 0, 1))
/ | | 1 | -------------- dx | 2 | x - 10*x + 29 | /
1 1 -------------- = ------------------ 2 / 2 \ x - 10*x + 29 |/ x 5\ | 4*||- - + -| + 1| \\ 2 2/ /
/ | | 1 | -------------- dx | 2 = | x - 10*x + 29 | /
/ | | 1 | -------------- dx | 2 | / x 5\ | |- - + -| + 1 | \ 2 2/ | / -------------------- 4
/ | | 1 | -------------- dx | 2 | / x 5\ | |- - + -| + 1 | \ 2 2/ | / -------------------- 4
5 x v = - - - 2 2
/ | | 1 | ------ dv | 2 | 1 + v | / atan(v) ------------ = ------- 4 4
/ | | 1 | -------------- dx | 2 | / x 5\ | |- - + -| + 1 | \ 2 2/ / 5 x\ | atan|- - + -| / \ 2 2/ -------------------- = ------------- 4 2
/ 5 x\ atan|- - + -| \ 2 2/ C + ------------- 2
/ / 5 x\ | atan|- - + -| | 1 \ 2 2/ | -------------- dx = C + ------------- | 2 2 | x - 10*x + 29 | /
atan(5/2) atan(2) --------- - ------- 2 2
=
atan(5/2) atan(2) --------- - ------- 2 2
atan(5/2)/2 - atan(2)/2
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.