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Question Number 201925 by Calculusboy last updated on 15/Dec/23

Commented by Calculusboy last updated on 17/Dec/23

$$\mathit{t}\mathit{h}\mathit{a}\mathit{n}\mathit{k}\mathit{s}\mathit{s}\mathit{i}\mathit{r}$$

Commented by Frix last updated on 16/Dec/23

$$=2\underset{0}{\stackrel{\frac{\pi }{4}}{\int }}\frac{{(1+{\tan }^{2}x)}^2}{1-\tan x+{\tan }^{2}x-{\tan }^{3}x+{\tan }^{4}x}dx$$$$\mathrm{Use}t=\tan x\mathrm{to}\mathrm{get}$$$$2\underset{0}{\stackrel{1}{\int }}\frac{t^2+1}{t^4-t^3+t^2-t+1}dt$$$$\mathrm{I}\mathrm{get}\frac{2\sqrt{5(5+2\sqrt{5})}}{25}\pi$$

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