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## Homework Statement

S xln(1+x)dx

## Homework Equations

## The Attempt at a Solution

S xln(1+x)dx

t = (1+x)

dt = dx

x = t-1

S (t-1)ln(t)dt

u = ln(t)

du = 1/t

dv = (t-1)dt

v =( t^2/2 - t)

uv - S vdu

ln(t)*( t^2/2 - t) - S ( t^2/2 - t)*1/t dt

distributing and solving integral

ln(t)*t^2/2 - ln(t)*t - (t^2/4 - t)

now putting the expression for t back in gives me something radically different from what the book tells me it is

my answer ln(1+x)*[(1+x)^2]/2 - ln(x+1)*(x+1) - [(1+x)^2]/4 - (x+1) + C

the books answer : 1/2*(x^2 - 1)*ln(x+1) - 1/4*x^2 + 1/2*x +3/4 + C

where have i gone wrong