1 / | | 1 | ----------------------- dx | 4*sin(x) + 3*cos(x) + 1 | / 0
Integral(1/(4*sin(x) + 3*cos(x) + 1), (x, 0, 1))
/ ___ / ___ /x\\ ___ / ___ /x\\ | \/ 6 *log|-2 - \/ 6 + tan|-|| \/ 6 *log|-2 + \/ 6 + tan|-|| | 1 \ \2// \ \2// | ----------------------- dx = C - ------------------------------ + ------------------------------ | 4*sin(x) + 3*cos(x) + 1 12 12 | /
___ / / ___ \\ ___ / ___\ ___ / / ___\\ ___ / ___ \ \/ 6 *\pi*I + log\2 + \/ 6 - tan(1/2)// \/ 6 *log\-2 + \/ 6 / \/ 6 *\pi*I + log\2 + \/ 6 // \/ 6 *log\-2 + \/ 6 + tan(1/2)/ - ---------------------------------------- - --------------------- + ----------------------------- + -------------------------------- 12 12 12 12
=
___ / / ___ \\ ___ / ___\ ___ / / ___\\ ___ / ___ \ \/ 6 *\pi*I + log\2 + \/ 6 - tan(1/2)// \/ 6 *log\-2 + \/ 6 / \/ 6 *\pi*I + log\2 + \/ 6 // \/ 6 *log\-2 + \/ 6 + tan(1/2)/ - ---------------------------------------- - --------------------- + ----------------------------- + -------------------------------- 12 12 12 12
-sqrt(6)*(pi*i + log(2 + sqrt(6) - tan(1/2)))/12 - sqrt(6)*log(-2 + sqrt(6))/12 + sqrt(6)*(pi*i + log(2 + sqrt(6)))/12 + sqrt(6)*log(-2 + sqrt(6) + tan(1/2))/12
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.