Question

How do you find the integral of `1/(x^(1/2))sin(x^(1/2))`?

Answer 1

`int1/x^(1/2)sin(x^(1/2))"d"x=-2cos(x^(1/2))+"c"`

Explanation:

Let `u=x^(1/2)` and `"d"u=1/(2x^(1/2))"d"x` so `2"d"u=1/(x^(1/2))"d"x`

Then

`int1/x^(1/2)sinx^(1/2)"d"x=2intsinu"d"u=-2cosu=-2cosx^(1/2)+"c"`