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Evaluate: ∫x/(x2 + 1)(x + 1) dx

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Let I = ∫x/(x2 + 1)(x + 1) dx

Now, x/(x2 + 1)(x + 1) = (1/2)[(x + 1)/(x2 + 1) - (1/x + 1)] (partial function)

So, I = (1/2)∫x/(x2 + 1) dx + ∫dx/(x2 + 1) - ∫dx/(x + 1)

= (1/4) log(x2 + 1) + 1/2) tan-1 x - (1/2) log|x + 1| + k

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