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Question Number 131053 by pipin last updated on 01/Feb/21

$$\int \frac{{\mathrm{x}}^2+2}{{\mathrm{x}}^4+4}\mathrm{dx}$$

Answered by Ar Brandon last updated on 01/Feb/21

$$\mathcal{I}=\int \frac{{\mathrm{x}}^2+2}{{\mathrm{x}}^4+4}\mathrm{dx}=\int \frac{1+\frac{2}{{\mathrm{x}}^2}}{{(\mathrm{x}-\frac{2}{\mathrm{x}})}^2+4}\mathrm{dx}$$$$=\frac{1}{2}{\tan }^{-1}\left(\frac{{\mathrm{x}}^2-2}{2\mathrm{x}}\right)+\mathcal{C}$$

Commented by pipin last updated on 01/Feb/21

$$\mathrm{wow},\mathrm{thank}\mathrm{you}\mathrm{bro}$$

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