1 / | | x | ----------- dx | ________ | / 4 | \/ 1 - x | / 0
Integral(x/sqrt(1 - x^4), (x, 0, 1))
// / 2\ \ / ||-I*acosh\x / | 4| | | ||------------- for |x | > 1| | x || 2 | | ----------- dx = C + |< | | ________ || / 2\ | | / 4 || asin\x / | | \/ 1 - x || -------- otherwise | | \\ 2 / /
1 / | | / -I*x 4 | |------------ for x > 1 | | _________ | | / 4 | |\/ -1 + x | < dx | | x | |----------- otherwise | | ________ | | / 4 | \\/ 1 - x | / 0
=
1 / | | / -I*x 4 | |------------ for x > 1 | | _________ | | / 4 | |\/ -1 + x | < dx | | x | |----------- otherwise | | ________ | | / 4 | \\/ 1 - x | / 0
Integral(Piecewise((-i*x/sqrt(-1 + x^4), x^4 > 1), (x/sqrt(1 - x^4), True)), (x, 0, 1))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.