1 / | | x + 2 | ------------ dx | 2 | x + 4*x + 8 | / 0
Integral((x + 2)/(x^2 + 4*x + 8), (x, 0, 1))
/ | | x + 2 | ------------ dx | 2 | x + 4*x + 8 | /
/ 2*x + 4 \ |------------| /0\ | 2 | |-| x + 2 \x + 4*x + 8/ \4/ ------------ = -------------- + -------------- 2 2 2 x + 4*x + 8 / x \ |- - - 1| + 1 \ 2 /
/ | | x + 2 | ------------ dx | 2 = | x + 4*x + 8 | /
/ | | 2*x + 4 | ------------ dx | 2 | x + 4*x + 8 | / ------------------ 2
/ | | 2*x + 4 | ------------ dx | 2 | x + 4*x + 8 | / ------------------ 2
2 u = x + 4*x
/ | | 1 | ----- du | 8 + u | / log(8 + u) ----------- = ---------- 2 2
/ | | 2*x + 4 | ------------ dx | 2 | x + 4*x + 8 | / 2 \ / log\8 + x + 4*x/ ------------------ = ----------------- 2 2
0
x v = -1 - - 2
True
True
/ 2 \ log\8 + x + 4*x/ C + ----------------- 2
/ | / 2 \ | x + 2 log\x + 4*x + 8/ | ------------ dx = C + ----------------- | 2 2 | x + 4*x + 8 | /
log(13) log(8) ------- - ------ 2 2
=
log(13) log(8) ------- - ------ 2 2
log(13)/2 - log(8)/2
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.