1 / | | 3 2 | x + x | --------------------- dx | 3 2 | 2*x - 5*x + 4*x - 4 | / 0
Integral((x^3 + x^2)/(2*x^3 - 5*x^2 + 4*x - 4), (x, 0, 1))
/ / ____ \ | ____ |4*\/ 15 *(-1/4 + x)| | 3 2 / 2\ \/ 15 *atan|-------------------| | x + x x log\2 - x + 2*x / 3*log(-2 + x) \ 15 / | --------------------- dx = C + - + ----------------- + ------------- + -------------------------------- | 3 2 2 8 2 12 | 2*x - 5*x + 4*x - 4 | /
/ ____\ / ____\ ____ |\/ 15 | ____ |\/ 15 | \/ 15 *atan|------| \/ 15 *atan|------| 1 3*log(2) log(3/2) \ 5 / \ 15 / - - -------- + -------- + ------------------- + ------------------- 2 2 8 12 12
=
/ ____\ / ____\ ____ |\/ 15 | ____ |\/ 15 | \/ 15 *atan|------| \/ 15 *atan|------| 1 3*log(2) log(3/2) \ 5 / \ 15 / - - -------- + -------- + ------------------- + ------------------- 2 2 8 12 12
1/2 - 3*log(2)/2 + log(3/2)/8 + sqrt(15)*atan(sqrt(15)/5)/12 + sqrt(15)*atan(sqrt(15)/15)/12
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.