Question

\[\int\limits_{2}^{e+1}\frac{ x }{ (x-1)^{2} } dx\]

Can anyone show me the steps to solving this definate intergral?

Answer 1

Do you know about partial fraction decomposition?

Answer 2

No, I do not but let me google it and see if it seems like something I have done before.

Answer 3

I think a substitution would be simpler (less work) here.
\[u=x-1\\
du=dx\]
\[\int_1^e\frac{u+1}{u^2}du\]