Perform the following integration

Question

Integral of x √ 2 − 4x dx

note: 2-4x is all under the square root

Answer 1

Substitution: 2 - 4x = u; x = (2 - u)/4 and du = - 4dx; dx = - du/4

∫x√2 - 4xdx = ∫(u - 2)/4·√u·du/4 =1/16∫(u^3/2 - 2u^1/2)du = 1/16(2/5u^5/2 - 2·2/3u^3/2) + C = 1/8u^3/2(u/5 - 2/3) + C

1/8(2 - 4x)^3/2((2 - 4x)/5 - 2/3) + C.