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Question Number 198806 by sonukgindia last updated on 24/Oct/23

Answered by Frix last updated on 24/Oct/23

$$\int \frac{7x^2+5}{x^4+6x^2+25}dx=$$$$=\int (\frac{3x+1}{2(x^2-2x+5)}-\frac{3x-1}{2(x^2+2x+5)})dx=$$$$=\int (\frac{2}{x^2-2x+5}+\frac{2}{x^2+2x+5}+\frac{3(x-1)}{2(x^2-2x+5)}-\frac{3(x+1)}{2(x^2+2x+5)})dx=$$$$={\tan }^{-1}\frac{x-1}{2}+{\tan }^{-1}\frac{x+1}{2}+\frac{3\ln (x^2-2x+5)}{4}-\frac{3\ln (x^2+2x+5)}{4}+C$$$$\Rightarrow \mathrm{answer}\mathrm{is}\pi$$

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