1 / | | d*x | -------- dx | 2 | 3*x + 5 | / 0
Integral((d*x)/(3*x^2 + 5), (x, 0, 1))
/ | | d*x | -------- dx | 2 | 3*x + 5 | /
/0\ |-| d*x d 3*2*x \5/ -------- = -*-------------- + ----------------- 2 6 2 2 3*x + 5 3*x + 0*x + 5 / ____ \ |-\/ 15 | |--------*x| + 1 \ 5 /
/ | | d*x | -------- dx | 2 = | 3*x + 5 | /
/ | | 3*2*x d* | -------------- dx | 2 | 3*x + 0*x + 5 | / ---------------------- 6
/ | | 3*2*x d* | -------------- dx | 2 | 3*x + 0*x + 5 | / ---------------------- 6
2 u = 3*x
/ | | 1 d* | ----- du | 5 + u | / d*log(5 + u) ------------- = ------------ 6 6
/ | | 3*2*x d* | -------------- dx | 2 | 3*x + 0*x + 5 | / 2\ / d*log\5 + 3*x / ---------------------- = --------------- 6 6
0
____ -x*\/ 15 v = ---------- 5
True
True
/ 2\ d*log\5 + 3*x / C + --------------- 6
/ | / 2\ | d*x d*log\5 + 3*x / | -------- dx = C + --------------- | 2 6 | 3*x + 5 | /
d*log(5) d*log(8) - -------- + -------- 6 6
=
d*log(5) d*log(8) - -------- + -------- 6 6
-d*log(5)/6 + d*log(8)/6
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.