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  • Integrate: ( x^2 -1 ) / x^3 squart root (2x^4 - 2x^2+1).

Integrate: ( x^2 -1 ) / x^3 squart root (2x^4 - 2x^2+1).

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Solution: We have ,

               I=int fracx^2-1x^3cdot sqrt2x^4-2x^2+1hspace0.2cmdx

             \ Rightarrow I= int fracx^2-1x^3cdot x^2sqrt2-frac2x^2+frac1x^4 dx\ \ Rightarrow I=int fracfrac1x^3-frac1x^5sqrt2-frac2x^2+frac1x^4 dx

           Put ,   (2-frac2x^2+frac1x^4)=tRightarrow (frac1x^3-frac1x^5)dx=frac14dt

                   \ Rightarrow I=frac14int t^frac12dt=frac12sqrtt+c\ \Rightarrow I=fracsqrt2x^4-2x^2+12x^2+c

    

Posted by

Deependra Verma

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