1 / | | x | -------- dx | 2 | 4*x + 5 | / 0
Integral(x/(4*x^2 + 5), (x, 0, 1))
/ | | x | -------- dx | 2 | 4*x + 5 | /
/ 4*2*x \ |--------------| /0\ | 2 | |-| x \4*x + 0*x + 5/ \5/ -------- = ---------------- + ----------------- 2 8 2 4*x + 5 / ___ \ |-2*\/ 5 | |--------*x| + 1 \ 5 /
/ | | x | -------- dx | 2 = | 4*x + 5 | /
/ | | 4*2*x | -------------- dx | 2 | 4*x + 0*x + 5 | / -------------------- 8
/ | | 4*2*x | -------------- dx | 2 | 4*x + 0*x + 5 | / -------------------- 8
2 u = 4*x
/ | | 1 | ----- du | 5 + u | / log(5 + u) ----------- = ---------- 8 8
/ | | 4*2*x | -------------- dx | 2 | 4*x + 0*x + 5 | / 2\ / log\5 + 4*x / -------------------- = ------------- 8 8
0
___ -2*x*\/ 5 v = ---------- 5
True
True
/ 2\ log\5 + 4*x / C + ------------- 8
/ | / 2\ | x log\5 + 4*x / | -------- dx = C + ------------- | 2 8 | 4*x + 5 | /
log(5) log(9) - ------ + ------ 8 8
=
log(5) log(9) - ------ + ------ 8 8
-log(5)/8 + log(9)/8
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.