1 / | | 1 | ------------------------- dx | _________ _________ | \/ 2*x - 3 + \/ 2*x + 5 | / 0
Integral(1/(sqrt(2*x - 3) + sqrt(2*x + 5)), (x, 0, 1))
// ___ __________ ___ 3/2 ___ __________ \ / || \/ 2 *\/ -3/2 + x \/ 2 *(5/2 + x) \/ 2 *\/ -3/2 + x *(5/2 + x) |5/2 + x| | | || ------------------ + ------------------ - ---------------------------- for --------- > 1| | 1 || 3 12 12 4 | | ------------------------- dx = C + |< | | _________ _________ || ___ 3/2 ___ _________ ___ _________ | | \/ 2*x - 3 + \/ 2*x + 5 ||\/ 2 *(5/2 + x) I*\/ 2 *\/ 3/2 - x I*\/ 2 *\/ 3/2 - x *(5/2 + x) | | ||------------------ + ------------------- - ----------------------------- otherwise | / \\ 12 3 12 /
___ ____ 2 6 I*\/ 7 I*\/ 15 - ------------------- + ------------- + ------------- - ------------------- ___ ___ ___ ___ ___ ___ 3*\/ 5 + 3*I*\/ 3 3*I + 3*\/ 7 3*I + 3*\/ 7 3*\/ 5 + 3*I*\/ 3
=
___ ____ 2 6 I*\/ 7 I*\/ 15 - ------------------- + ------------- + ------------- - ------------------- ___ ___ ___ ___ ___ ___ 3*\/ 5 + 3*I*\/ 3 3*I + 3*\/ 7 3*I + 3*\/ 7 3*\/ 5 + 3*I*\/ 3
-2/(3*sqrt(5) + 3*i*sqrt(3)) + 6/(3*i + 3*sqrt(7)) + i*sqrt(7)/(3*i + 3*sqrt(7)) - i*sqrt(15)/(3*sqrt(5) + 3*i*sqrt(3))
(0.305829970414716 - 0.174839684279443j)
(0.305829970414716 - 0.174839684279443j)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.