evaluate $\int \frac{x^2\cdot\log(x)}{x+1} dx$

I am trying to evaluate integral:

$$\int \frac{x^2\log(x)}{x+1}dx$$

But I have some problems with it. If I use Wolfram Alpha like this I get a result, but I need evaluate it by hand. Which method should I use?

If we represent it as:

$$\int(x^2\log(x)\cdot d(\ln(x))dx$$

then it is unclear what to dot here, even we can represent as power, take $x^2$ in power of $\log(x)$, not hint yet. Please help me to evaluate it.

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The summation runs over $j$ while the summands are in terms of $k$, so, the infinite sum diverges. No? Or I guess it's a typo. [Didn't go through the answer, so apologies if wrong!] –  user21436 Jan 21 '12 at 11:48