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