1 / | | 1 | ------------------- dx | 2*cos(x) + 3*sin(x) | / 0
Integral(1/(2*cos(x) + 3*sin(x)), (x, 0, 1))
/ ____ \ / ____ \ / ____ | 3 \/ 13 /x\| ____ | 3 \/ 13 /x\| | \/ 13 *log|- - - ------ + tan|-|| \/ 13 *log|- - + ------ + tan|-|| | 1 \ 2 2 \2// \ 2 2 \2// | ------------------- dx = C - --------------------------------- + --------------------------------- | 2*cos(x) + 3*sin(x) 13 13 | /
/ / ____ \\ / ____\ / / ____\\ / ____ \ ____ | |3 \/ 13 || ____ | 3 \/ 13 | ____ | |3 \/ 13 || ____ | 3 \/ 13 | \/ 13 *|pi*I + log|- + ------ - tan(1/2)|| \/ 13 *log|- - + ------| \/ 13 *|pi*I + log|- + ------|| \/ 13 *log|- - + ------ + tan(1/2)| \ \2 2 // \ 2 2 / \ \2 2 // \ 2 2 / - ------------------------------------------ - ------------------------ + ------------------------------- + ----------------------------------- 13 13 13 13
=
/ / ____ \\ / ____\ / / ____\\ / ____ \ ____ | |3 \/ 13 || ____ | 3 \/ 13 | ____ | |3 \/ 13 || ____ | 3 \/ 13 | \/ 13 *|pi*I + log|- + ------ - tan(1/2)|| \/ 13 *log|- - + ------| \/ 13 *|pi*I + log|- + ------|| \/ 13 *log|- - + ------ + tan(1/2)| \ \2 2 // \ 2 2 / \ \2 2 // \ 2 2 / - ------------------------------------------ - ------------------------ + ------------------------------- + ----------------------------------- 13 13 13 13
-sqrt(13)*(pi*i + log(3/2 + sqrt(13)/2 - tan(1/2)))/13 - sqrt(13)*log(-3/2 + sqrt(13)/2)/13 + sqrt(13)*(pi*i + log(3/2 + sqrt(13)/2))/13 + sqrt(13)*log(-3/2 + sqrt(13)/2 + tan(1/2))/13
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.