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$\displaystyle\int_0^1\frac{2t+i}{t^2+it^2+1}dt = \int_0^1\frac{2t^3+3t+i-it^2}{t^4+3t^2+1}dt =\int_0^1\frac{2t^3+3t}{t^4+3t^2+1}dt+i\int_0^1 \frac{1-t^2}{t^4+3t^2+1}dt$

I tried multiplying through by the conjugate but that didn't seem fruitful and left me with the above expression. Is there a better way to tackle this problem?

Typo I mixed up two parts

I tried multiplying through by the conjugate but that didn't seem fruitful and left me with the above expression. Is there a better way to tackle this problem?

Typo I mixed up two parts

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