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  • Integrate: 1 / x square root (x^6 -16 )

Integrate: 1 / x square root (x^6 -16 )

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Solution:

                     I=int frac1xsqrtx^6-16dx=int fracx^2x^3sqrtx^6-16dx

                      Putting           x^3=tRightarrow 3x^2dx=dt

                    \ \ Rightarrow frac13int frac1tsqrtt^2-16dt=frac148int frac1fract4sqrtfract^216-1dt\ \ Rightarrow I=frac112sec fract4+c=frac112sec fracx^34+c.

       

Posted by

Deependra Verma

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