Evaluate the integral of x*ln(1+x) dx by first making a substitution and then using integration by parts.
I let u=1+x and du = dx but then ln(u) du can't integrate to anything?
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1 answer

you need to get rid of that pesky ln(1+x). So,
u = ln(1+x)
du = 1/(1+x) dx
dv = x dx
v = 1/2 x^2
∫u dv = uv  ∫v du
= 1/2 x^2 ln(1+x)  1/2 ∫x^2/(1+x) dx
which is not so hard, eh? 👍
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answered by Steve
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