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Integrate: ( x - x^3)^1/3 /(x^4)

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Solution: We have ,  

                 I=int frac(x-x^3)^1/3x^4dx

          \Rightarrow I=int frac(frac1x^2-1)^1/3x^3dx    Put ,    (frac1x^2-1)=tRightarrow frac1x^3dx=-frac12dt

         Rightarrow     I=-frac12int t^1/3dt=-frac38t^4/3+c

        Rightarrow          I=-frac38(frac1x^2-1)^4/3+c.

Posted by

Deependra Verma

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