1 / | | 5 - x | -------- dx | 2 | 3*x + 1 | / 0
Integral((5 - x)/(3*x^2 + 1), (x, 0, 1))
/ | | 5 - x | -------- dx | 2 | 3*x + 1 | /
/ 3*2*x \ |--------------| /5\ | 2 | |-| 5 - x \3*x + 0*x + 1/ \1/ -------- = - ---------------- + --------------- 2 6 2 3*x + 1 / ___ \ \-\/ 3 *x/ + 1
/ | | 5 - x | -------- dx | 2 = | 3*x + 1 | /
/ | | 3*2*x | -------------- dx | 2 / | 3*x + 0*x + 1 | | | 1 / 5* | --------------- dx - -------------------- | 2 6 | / ___ \ | \-\/ 3 *x/ + 1 | /
/ | | 3*2*x - | -------------- dx | 2 | 3*x + 0*x + 1 | / ---------------------- 6
2 u = 3*x
/ | | 1 - | ----- du | 1 + u | / -log(1 + u) ------------- = ------------ 6 6
/ | | 3*2*x - | -------------- dx | 2 | 3*x + 0*x + 1 | / 2\ / -log\1 + 3*x / ---------------------- = --------------- 6 6
/ | | 1 5* | --------------- dx | 2 | / ___ \ | \-\/ 3 *x/ + 1 | /
___ v = -x*\/ 3
/ | | 1 5* | ------ dv = 5*atan(v) | 2 | 1 + v | /
/ | ___ / ___\ | 1 5*\/ 3 *atan\x*\/ 3 / 5* | --------------- dx = --------------------- | 2 3 | / ___ \ | \-\/ 3 *x/ + 1 | /
/1 2\ log|- + x | ___ / ___\ \3 / 5*\/ 3 *atan\x*\/ 3 / C - ----------- + --------------------- 6 3
/ | / 2\ ___ / ___\ | 5 - x log\1 + 3*x / 5*\/ 3 *atan\x*\/ 3 / | -------- dx = C - ------------- + --------------------- | 2 6 3 | 3*x + 1 | /
___ log(3) log(4/3) 5*pi*\/ 3 - ------ - -------- + ---------- 6 6 9
=
___ log(3) log(4/3) 5*pi*\/ 3 - ------ - -------- + ---------- 6 6 9
-log(3)/6 - log(4/3)/6 + 5*pi*sqrt(3)/9
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.