Question-198806

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

Answered by Frix last updated on 24/Oct/23

\int \frac{7 x^{2} + 5}{x^{4} + 6 x^{2} + 25} d x =

= \int (\frac{3 x + 1}{2 (x^{2} - 2 x + 5)} - \frac{3 x - 1}{2 (x^{2} + 2 x + 5)}) d x =

= \int (\frac{2}{x^{2} - 2 x + 5} + \frac{2}{x^{2} + 2 x + 5} + \frac{3 (x - 1)}{2 (x^{2} - 2 x + 5)} - \frac{3 (x + 1)}{2 (x^{2} + 2 x + 5)}) d x =

= \tan^{- 1} \frac{x - 1}{2} + \tan^{- 1} \frac{x + 1}{2} + \frac{3 \ln (x^{2} - 2 x + 5)}{4} - \frac{3 \ln (x^{2} + 2 x + 5)}{4} + C

\Rightarrow answer is π

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