2 / | | x | ------------- dx | 2 | x + 2*x + 10 | / -1
Integral(x/(x^2 + 2*x + 10), (x, -1, 2))
/ | | x | ------------- dx | 2 | x + 2*x + 10 | /
/ 2*x + 2 \ |-------------| /-1 \ | 2 | |---| x \x + 2*x + 10/ \ 9 / ------------- = --------------- + -------------- 2 2 2 x + 2*x + 10 / x 1\ |- - - -| + 1 \ 3 3/
/ | | x | ------------- dx | 2 = | x + 2*x + 10 | /
/ | / | 1 | | -------------- dx | 2*x + 2 | 2 | ------------- dx | / x 1\ | 2 | |- - - -| + 1 | x + 2*x + 10 | \ 3 3/ | | / / ------------------- - -------------------- 2 9
/ | | 2*x + 2 | ------------- dx | 2 | x + 2*x + 10 | / ------------------- 2
2 u = x + 2*x
/ | | 1 | ------ du | 10 + u | / log(10 + u) ------------ = ----------- 2 2
/ | | 2*x + 2 | ------------- dx | 2 | x + 2*x + 10 | / 2 \ / log\10 + x + 2*x/ ------------------- = ------------------ 2 2
/ | | 1 - | -------------- dx | 2 | / x 1\ | |- - - -| + 1 | \ 3 3/ | / ---------------------- 9
1 x v = - - - - 3 3
/ | | 1 - | ------ dv | 2 | 1 + v | / -atan(v) -------------- = --------- 9 9
/ | | 1 - | -------------- dx | 2 | / x 1\ | |- - - -| + 1 | \ 3 3/ /1 x\ | -atan|- + -| / \3 3/ ---------------------- = ------------- 9 3
/1 x\ / 2 \ atan|- + -| log\10 + x + 2*x/ \3 3/ C + ------------------ - ----------- 2 3
/ /1 x\ | / 2 \ atan|- + -| | x log\10 + x + 2*x/ \3 3/ | ------------- dx = C + ------------------ - ----------- | 2 2 3 | x + 2*x + 10 | /
log(18) log(9) pi ------- - ------ - -- 2 2 12
=
log(18) log(9) pi ------- - ------ - -- 2 2 12
log(18)/2 - log(9)/2 - pi/12
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.