1 / | | 3 | x | ------ dx | 6 | 4 + x | / 0
Integral(x^3/(4 + x^6), (x, 0, 1))
/ / ___ 3 ___ ___ 2\ | 3 ___ ___ | \/ 3 \/ 2 *\/ 3 *x | | 3 3 ___ / 2/3 2\ 3 ___ / 4 3 ___ 2/3 2\ \/ 2 *\/ 3 *atan|- ----- + --------------| | x \/ 2 *log\2 + x / \/ 2 *log\x + 2*\/ 2 - 2 *x / \ 3 3 / | ------ dx = C - -------------------- + --------------------------------- + ------------------------------------------ | 6 12 24 12 | 4 + x | /
/ ___ 3 ___ ___\ 3 ___ ___ |\/ 3 \/ 2 *\/ 3 | 3 ___ / 2/3\ 3 ___ / 3 ___\ 3 ___ / 2/3\ 3 ___ / 2/3 3 ___\ \/ 2 *\/ 3 *atan|----- - -----------| 3 ___ ___ \/ 2 *log\1 + 2 / \/ 2 *log\2*\/ 2 / \/ 2 *log\2 / \/ 2 *log\1 - 2 + 2*\/ 2 / \ 3 3 / pi*\/ 2 *\/ 3 - ------------------- - ------------------ + --------------- + ----------------------------- - ------------------------------------- + -------------- 12 24 12 24 12 72
=
/ ___ 3 ___ ___\ 3 ___ ___ |\/ 3 \/ 2 *\/ 3 | 3 ___ / 2/3\ 3 ___ / 3 ___\ 3 ___ / 2/3\ 3 ___ / 2/3 3 ___\ \/ 2 *\/ 3 *atan|----- - -----------| 3 ___ ___ \/ 2 *log\1 + 2 / \/ 2 *log\2*\/ 2 / \/ 2 *log\2 / \/ 2 *log\1 - 2 + 2*\/ 2 / \ 3 3 / pi*\/ 2 *\/ 3 - ------------------- - ------------------ + --------------- + ----------------------------- - ------------------------------------- + -------------- 12 24 12 24 12 72
-2^(1/3)*log(1 + 2^(2/3))/12 - 2^(1/3)*log(2*2^(1/3))/24 + 2^(1/3)*log(2^(2/3))/12 + 2^(1/3)*log(1 - 2^(2/3) + 2*2^(1/3))/24 - 2^(1/3)*sqrt(3)*atan(sqrt(3)/3 - 2^(1/3)*sqrt(3)/3)/12 + pi*2^(1/3)*sqrt(3)/72
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.