Evaluate: `int(e^(sqrt(2))"cos"(e^(sqrt(x))))/(sqrt(x))dx`

Explanation

`I=inte^(sqrt2)(cos sqrtx)/(sqrtx)dx,`

put `z=sqrtx`

`implies(dz)/(dx)=(dx^(1//2))/(dx)`

`implies(dx)/(dz)=(1)/(2)*x^(1//2-1)=(1)/(2)*x^(-1//2)dx`

`implies2dz=(1)/(sqrtx)dx=(d x)/(z)`

`2zdz=dx`

`I=e^(sqrt2)int(cos z)/(z)xx2z*dz`

`=2e^(sqrt2)int cosz dx`

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