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