Question
need some help im doin antiderivatives it has (2-x^2)^4xdx i understand how to do it for the most part but i come up with 1/5(2-x^2)^5+c the book has a answer of -1/10(2-x^2)^5+c how what am i doing wrong
Answers
Steve
You may have forgotten a factor of -2:
∫(2-x^2)^4 x dx
if u = (2-x^2), du = -2x dx, so the integral is
∫u^4 (-1/2) du
= 1/5 (2-x^2)^5 (-1/2) + c
because you started out with x dx, but needed -2x dx to get du.
∫(2-x^2)^4 x dx
if u = (2-x^2), du = -2x dx, so the integral is
∫u^4 (-1/2) du
= 1/5 (2-x^2)^5 (-1/2) + c
because you started out with x dx, but needed -2x dx to get du.