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