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