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\int \frac{2x+1}{\sqrt{3+2x-x^{2}}}dx

 

 

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I = \int \frac{2x+1}{\sqrt{3+2x-x^{2}}}dx
 

I = \int -\frac{2-2x-3}{\sqrt{3+2x-x^{2}}}dx

Let 3+2x -x2 = t2

(2 -2x)dx = 2t dt

I = \int-\frac{2t}{t} dt +\frac{3}{\sqrt{3+2x-x^{2}}}dx

I = -t +\int \frac{3}{\sqrt{2^2-(x-1)^2}}dx

I = -\sqrt{3+2x-x^2} + 3 \sin^{-1} \frac{x-1}{2}+c

Posted by

Safeer PP

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