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