Question

please solve this integration​

Answer 1

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Answer 2

$\LARGE\underline{\bf{\red{Answer}}}$

$\displaystyle\sf\int\dfrac{dx}{5-8x-x^2}$

$\displaystyle\sf=\int\dfrac{dx}{5-(8x+x^2)}$

$\displaystyle\sf = \int\dfrac{dx}{5-(x^2+8x+16-16)}$

$\displaystyle\sf = \int\dfrac{dx}{21-(x+4)^2}$

$\displaystyle\sf = \int\dfrac{dx}{\sqrt{21} -(x+4)^2}$

$\displaystyle\sf = \dfrac{1}{2\sqrt{22}} \: log \left|\dfrac{\sqrt{21}+(x+4)}{\sqrt{21}-(x+4)}\right| + C$

$\displaystyle\boxed{\sf = \dfrac{1}{2\sqrt{22}} \: log \left|\dfrac{\sqrt{21}+x+4}{\sqrt{21}-x+4}\right| + C}$

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