" Life is not a problem to be solved but a reality to be experienced! "
© Copyright 2013 - 2024 KUDO.TIPS - All rights reserved.
v = -2x
int x / (u - x^2)^3/2
= -1/2 int 1/v^3/2
= -1/2 x -2 v^-1/2 + C
= 1/akar (v) + C
= 1/ akar(u - x^2) + C
= Int x(u - x^2)^(-3/2) dx
Misal : P = u - x^2
=> dP = -2x dx => dx = dP/(-2x)
Int x(u - x^2)^(-3/2) dx
= Int x . P^(-3/2) dP/(-2x)
= Int -1/2 P^(-3/2) dP
= (-1/2)/(-1/2) P^(-1/2) + C
= 1/P^(1/2) + C
= 1/√P + C
= 1/√(u - x^2) + C