1 / | | 1 | ------------ dx | 2 | 2 - x + 6*x | / 0
Integral(1/(2 - x^2 + 6*x), (x, 0, 1))
// / ____ \ \ || ____ |\/ 11 *(-3 + x)| | ||-\/ 11 *acoth|---------------| | / || \ 11 / 2 | | ||------------------------------- for (-3 + x) > 11| | 1 || 11 | | ------------ dx = C - |< | | 2 || / ____ \ | | 2 - x + 6*x || ____ |\/ 11 *(-3 + x)| | | ||-\/ 11 *atanh|---------------| | / || \ 11 / 2 | ||------------------------------- for (-3 + x) < 11| \\ 11 /
____ / / ____\\ ____ / ____\ ____ / / ____\\ ____ / ____\ \/ 11 *\pi*I + log\2 + \/ 11 // \/ 11 *log\-3 + \/ 11 / \/ 11 *\pi*I + log\3 + \/ 11 // \/ 11 *log\-2 + \/ 11 / - ------------------------------- - ----------------------- + ------------------------------- + ----------------------- 22 22 22 22
=
____ / / ____\\ ____ / ____\ ____ / / ____\\ ____ / ____\ \/ 11 *\pi*I + log\2 + \/ 11 // \/ 11 *log\-3 + \/ 11 / \/ 11 *\pi*I + log\3 + \/ 11 // \/ 11 *log\-2 + \/ 11 / - ------------------------------- - ----------------------- + ------------------------------- + ----------------------- 22 22 22 22
-sqrt(11)*(pi*i + log(2 + sqrt(11)))/22 - sqrt(11)*log(-3 + sqrt(11))/22 + sqrt(11)*(pi*i + log(3 + sqrt(11)))/22 + sqrt(11)*log(-2 + sqrt(11))/22
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.