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