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Q16  Integrate the functions \frac{4x+1 }{\sqrt {2x ^ 2 + x -3 }}

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best_answer

let 
\\4x+1 = A\frac{d}{dx}(2x^2+x-3)+B\\ 4x+1=A(4x+1)+B\\ 4x+1=4Ax+A+B

 By equating the coefficient of x and constant term on each side, we get 
A = 1 and B=0

Let (2x^2+x-3) = t\Rightarrow (4x+1)dx =dt

\therefore \int \frac{4x+1}{\sqrt{2x^2+x-3}}dx= \int\frac{1}{\sqrt{t}}dt
                                                \\= 2\sqrt{t}+C\\ =2\sqrt{2x^2+x-3}+C
 

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manish

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