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