1 / | | 1 | ------------- dx | 2 | (cos(x) + 2) | / 0
Integral(1/((cos(x) + 2)^2), (x, 0, 1))
/ /x pi\ / ___ /x\\\ / /x pi\ / ___ /x\\\ | |- - --| |\/ 3 *tan|-||| | |- - --| |\/ 3 *tan|-||| / /x\ ___ | |2 2 | | \2/|| ___ 2/x\ | |2 2 | | \2/|| | 6*tan|-| 12*\/ 3 *|pi*floor|------| + atan|------------|| 4*\/ 3 *tan |-|*|pi*floor|------| + atan|------------|| | 1 \2/ \ \ pi / \ 3 // \2/ \ \ pi / \ 3 // | ------------- dx = C - -------------- + ------------------------------------------------ + ------------------------------------------------------- | 2 2/x\ 2/x\ 2/x\ | (cos(x) + 2) 27 + 9*tan |-| 27 + 9*tan |-| 27 + 9*tan |-| | \2/ \2/ \2/ /
/ / ___ \\ / / ___ \\ ___ | |\/ 3 *tan(1/2)|| ___ 2 | |\/ 3 *tan(1/2)|| ___ 12*\/ 3 *|-pi + atan|--------------|| 4*\/ 3 *tan (1/2)*|-pi + atan|--------------|| 6*tan(1/2) 4*pi*\/ 3 \ \ 3 // \ \ 3 // - ---------------- + ---------- + ------------------------------------- + ---------------------------------------------- 2 9 2 2 27 + 9*tan (1/2) 27 + 9*tan (1/2) 27 + 9*tan (1/2)
=
/ / ___ \\ / / ___ \\ ___ | |\/ 3 *tan(1/2)|| ___ 2 | |\/ 3 *tan(1/2)|| ___ 12*\/ 3 *|-pi + atan|--------------|| 4*\/ 3 *tan (1/2)*|-pi + atan|--------------|| 6*tan(1/2) 4*pi*\/ 3 \ \ 3 // \ \ 3 // - ---------------- + ---------- + ------------------------------------- + ---------------------------------------------- 2 9 2 2 27 + 9*tan (1/2) 27 + 9*tan (1/2) 27 + 9*tan (1/2)
-6*tan(1/2)/(27 + 9*tan(1/2)^2) + 4*pi*sqrt(3)/9 + 12*sqrt(3)*(-pi + atan(sqrt(3)*tan(1/2)/3))/(27 + 9*tan(1/2)^2) + 4*sqrt(3)*tan(1/2)^2*(-pi + atan(sqrt(3)*tan(1/2)/3))/(27 + 9*tan(1/2)^2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.