1 / | | x + 4 | ------------ dx | 2 | x + 2*x + 5 | / 0
Integral((x + 4)/(x^2 + 2*x + 5), (x, 0, 1))
/ | | x + 4 | ------------ dx | 2 | x + 2*x + 5 | /
/ 2*x + 2 \ |------------| /3\ | 2 | |-| x + 4 \x + 2*x + 5/ \4/ ------------ = -------------- + -------------- 2 2 2 x + 2*x + 5 / x 1\ |- - - -| + 1 \ 2 2/
/ | | x + 4 | ------------ dx | 2 = | x + 2*x + 5 | /
/ | / | 1 | 3* | -------------- dx | 2*x + 2 | 2 | ------------ dx | / x 1\ | 2 | |- - - -| + 1 | x + 2*x + 5 | \ 2 2/ | | / / ------------------ + ---------------------- 2 4
/ | | 2*x + 2 | ------------ dx | 2 | x + 2*x + 5 | / ------------------ 2
2 u = x + 2*x
/ | | 1 | ----- du | 5 + u | / log(5 + u) ----------- = ---------- 2 2
/ | | 2*x + 2 | ------------ dx | 2 | x + 2*x + 5 | / 2 \ / log\5 + x + 2*x/ ------------------ = ----------------- 2 2
/ | | 1 3* | -------------- dx | 2 | / x 1\ | |- - - -| + 1 | \ 2 2/ | / ---------------------- 4
1 x v = - - - - 2 2
/ | | 1 3* | ------ dv | 2 | 1 + v | / 3*atan(v) -------------- = --------- 4 4
/ | | 1 3* | -------------- dx | 2 | / x 1\ | |- - - -| + 1 | \ 2 2/ /1 x\ | 3*atan|- + -| / \2 2/ ---------------------- = ------------- 4 2
/1 x\ / 2 \ 3*atan|- + -| log\5 + x + 2*x/ \2 2/ C + ----------------- + ------------- 2 2
/ /1 x\ | / 2 \ 3*atan|- + -| | x + 4 log\5 + x + 2*x/ \2 2/ | ------------ dx = C + ----------------- + ------------- | 2 2 2 | x + 2*x + 5 | /
log(8) 3*atan(1/2) log(5) 3*pi ------ - ----------- - ------ + ---- 2 2 2 8
=
log(8) 3*atan(1/2) log(5) 3*pi ------ - ----------- - ------ + ---- 2 2 2 8
log(8)/2 - 3*atan(1/2)/2 - log(5)/2 + 3*pi/8
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.