Evaluate the indefinite integral of Int(x/(x+8)^(1/4))?

Answer 1

try

t^4 = (x+8)

x = (t^4) - 8

dx = 4 (t^3) dt

[ { x dx }/ (x+8)^(1/4) ] = [{ ( (t^4) - 8 )4 (t^3) dt} / t ]

Answer 2

Try u = x+8, x = u-8, dx = du.
So you get
∫ (u-8)*u^-(1/4) du
= ∫ u^(3/4)- 8u^(-1/4) du
= 4/7 u^(7/4) - 32/3 u^3/4 + C
= 4/7(x+8)^7/4 -32/3(x+8)^3/4 + C.