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