Integral x root 4x+1

partial integral !!
Good answer *5

Let I = ∫{xdx/sq rt(4x+1)] put 4x+ 1 = t^2 or 4dx = 2t*dt or dx = t*dt/(2) and x = (t^2 -1)/4 or
I = (1/8)∫{t(t^2-1)dt/t] = (1/8)∫(t^2-1)dt] = t^3/24 - t/8 + C = (1/24)*[{4x+1}^(3/2)] - (1/8)sq rt(4x+1)+ C
= sq rt(4x+1)[(x/6)+ (1/24) - (1/8)] + C = sq rt(4x+1)[(x/6) - (1/12)] + C
=(1/12)*(2x-1)*sq rt(4x+1) + C