1 / | | 7 | acot (3)*x | ---------- dx | 2 | 1 + 9*x | / 0
Integral((acot(3)^7*x)/(1 + 9*x^2), (x, 0, 1))
/ | | 7 | acot (3)*x | ---------- dx | 2 | 1 + 9*x | /
/0\ 7 7 |-| acot (3)*x acot (3) 9*2*x \1/ ---------- = --------*-------------- + ----------- 2 18 2 2 1 + 9*x 9*x + 0*x + 1 (-3*x) + 1
/ | | 7 | acot (3)*x | ---------- dx = | 2 | 1 + 9*x | /
/ | 7 | 9*2*x acot (3)* | -------------- dx | 2 | 9*x + 0*x + 1 | / ----------------------------- 18
/ | 7 | 9*2*x acot (3)* | -------------- dx | 2 | 9*x + 0*x + 1 | / ----------------------------- 18
2 u = 9*x
/ | 7 | 1 acot (3)* | ----- du | 1 + u | 7 / acot (3)*log(1 + u) -------------------- = ------------------- 18 18
/ | 7 | 9*2*x acot (3)* | -------------- dx | 2 | 9*x + 0*x + 1 | 7 / 2\ / acot (3)*log\1 + 9*x / ----------------------------- = ---------------------- 18 18
0
v = -3*x
True
True
7 / 2\ acot (3)*log\1 + 9*x / C + ---------------------- 18
/ | | 7 7 / 2\ | acot (3)*x acot (3)*log\1 + 9*x / | ---------- dx = C + ---------------------- | 2 18 | 1 + 9*x | /
7 acot (3)*log(10) ---------------- 18
=
7 acot (3)*log(10) ---------------- 18
acot(3)^7*log(10)/18
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.