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