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