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Integrate: x / ( x^2 -a^2 ) ( x^2 - b^2 )

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Solution: 

                  I=int fracx(x^2-a^2)(x^2-b^2)dx      Put   x^2=yRightarrow 2xdx=dy,

        Rightarrow     I=frac12int frac1(y-a^2)(y-b^2)dy=frac12(a^2-b^2)int [frac1y-a^2-frac1y-b^2]dy

      Rightarrow      I=frac12(a^2-b^2)[log (y-a^2)-log (y-b^2)]+c

     Rightarrow                      I=frac12(a^2-b^2)log (fracx^2-a^2x^2-b^2)+c.   

Posted by

Deependra Verma

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