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Integrate: e^ square root (x) cos (e^square root x ) dx / square root (x)

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Solution:    We have , 

                    I=int frace^sqrtxcos (e^sqrtx)sqrtxdx

            Substituting         e^sqrtx=yRightarrow frac12sqrtxe^sqrtxdx=dy

          \ \ 	herefore I=int 2cos y dy =2sin y+c.

       Rightarrow     I=2sin (e^sqrtx)+c.  

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Deependra Verma

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