1 / | | 4 _________ | x *\/ 1 - x*x dx | / 0
Integral(x^4*sqrt(1 - x*x), (x, 0, 1))
/ | // 3/2 ________ \ | 4 _________ || 3 / 2\ / 2 / 2\ | | x *\/ 1 - x*x dx = C + |-1, x < 1)| / \\ 16 6 16 /
1 / | | / 4 8 2 2 4 6 6 | | 25*I*x I*x I*x I*x I*x 5*I*x 7*I*x 2 | |- --------------- - -------------- - --------------- - --------------- + --------------- + --------------- + -------------- for x > 1 | | _________ 3/2 3/2 _________ 3/2 3/2 _________ | | / 2 / 2\ / 2\ / 2 / 2\ / 2\ / 2 | | 24*\/ -1 + x 6*\-1 + x / 16*\-1 + x / 16*\/ -1 + x 48*\-1 + x / 24*\-1 + x / 6*\/ -1 + x | < dx | | 6 8 2 2 4 6 4 | | 7*x x x x x 5*x 25*x | | - ------------- - ------------- - -------------- + -------------- + -------------- + -------------- + -------------- otherwise | | ________ 3/2 3/2 ________ 3/2 3/2 ________ | | / 2 / 2\ / 2\ / 2 / 2\ / 2\ / 2 | \ 6*\/ 1 - x 6*\1 - x / 16*\1 - x / 16*\/ 1 - x 48*\1 - x / 24*\1 - x / 24*\/ 1 - x | / 0
=
1 / | | / 4 8 2 2 4 6 6 | | 25*I*x I*x I*x I*x I*x 5*I*x 7*I*x 2 | |- --------------- - -------------- - --------------- - --------------- + --------------- + --------------- + -------------- for x > 1 | | _________ 3/2 3/2 _________ 3/2 3/2 _________ | | / 2 / 2\ / 2\ / 2 / 2\ / 2\ / 2 | | 24*\/ -1 + x 6*\-1 + x / 16*\-1 + x / 16*\/ -1 + x 48*\-1 + x / 24*\-1 + x / 6*\/ -1 + x | < dx | | 6 8 2 2 4 6 4 | | 7*x x x x x 5*x 25*x | | - ------------- - ------------- - -------------- + -------------- + -------------- + -------------- + -------------- otherwise | | ________ 3/2 3/2 ________ 3/2 3/2 ________ | | / 2 / 2\ / 2\ / 2 / 2\ / 2\ / 2 | \ 6*\/ 1 - x 6*\1 - x / 16*\1 - x / 16*\/ 1 - x 48*\1 - x / 24*\1 - x / 24*\/ 1 - x | / 0
Integral(Piecewise((-25*i*x^4/(24*sqrt(-1 + x^2)) - i*x^8/(6*(-1 + x^2)^(3/2)) - i*x^2/(16*(-1 + x^2)^(3/2)) - i*x^2/(16*sqrt(-1 + x^2)) + i*x^4/(48*(-1 + x^2)^(3/2)) + 5*i*x^6/(24*(-1 + x^2)^(3/2)) + 7*i*x^6/(6*sqrt(-1 + x^2)), x^2 > 1), (-7*x^6/(6*sqrt(1 - x^2)) - x^8/(6*(1 - x^2)^(3/2)) - x^2/(16*(1 - x^2)^(3/2)) + x^2/(16*sqrt(1 - x^2)) + x^4/(48*(1 - x^2)^(3/2)) + 5*x^6/(24*(1 - x^2)^(3/2)) + 25*x^4/(24*sqrt(1 - x^2)), True)), (x, 0, 1))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.