Find:
      \int \frac{dx}{\sqrt{5-4x-2x^{2}}}

 

 

 

 
 
 
 
 

Answers (1)

I= \int \frac{dx}{\sqrt{5-4x-2x^{2}}}
   I= \frac{1}{\sqrt{2}}\int \frac{dx}{\sqrt{-\left ( x^{2}+2x-\frac{5}{2} \right )}}= \frac{1}{\sqrt{2}}\int \frac{dx}{\sqrt{-\left ( x^{2}+2x+1^{2}-\frac{5}{2}-1 \right )}}
       I= \frac{1}{\sqrt{2}}\int \frac{dx}{\sqrt{\left ( \sqrt{\frac{7}{2}} \right )^{2}-\left ( x+1 \right )^{2}}}= \frac{1}{\sqrt{2}}\sin^{-1}\frac{x+1}{\sqrt{\frac{7}{2}}}
or \frac{1}{\sqrt{2}}\sin^{-1}\left ( \frac{\sqrt{2}\left ( x+1 \right )}{\sqrt{7}} \right )+c

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