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