(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[itex]\int^{√x}_{1}[/itex][itex]\frac{t^{3}+t-1}{t^{2}(t^{2}+1)}[/itex] dt

2. Relevant equations

3. The attempt at a solution

So I first start by expanding the bottom part of the fraction to t[itex]^{4}[/itex]+t[itex]^{2}[/itex], and letting u equal to that. Then du=4t[itex]^{3}[/itex]+2t dt. I move the common multiple of 2 over to the other side so that it is (1/2)du=2t[itex]^{3}[/itex]+t dt. I cannot find out how to relate that to the numerator (although I am so close).

Can someone please help? Thanks!

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# Evaluate integral of a polynomial over another polynomial (complicated substitution)

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