I am having trouble finding step 3. First correct answer will get full rating! T

Question

I am having trouble finding step 3. First correct answer will get full rating! Thanks!

Use a combination of substitution and parts to evaluate the integral : Substitution, let . Note: We use w here for the substitution instead of the more common variable u, since it is convenient for us to reserve u and v for the upcoming integration by parts. It follows that . To successfully continue with substitution, it is now necessary to rewrite dx strictly in terms of w. Thus dx = f(w)dw, where f(w) = . Complete the substitution, to get where g(w) = . Use integration by parts to integrate . Let u = and dv = sin(w)dw. This gives (as a function of w), . Substitute .

Explanation / Answer

integration[ sin(5sqrt(x)) ]dx

= -2*5*sqrt(x) /25 * cos(5*sqrt(x)) + (2/25) * sin(5*sqrt(x)) + C

= -2*sqrt(x) /5 * cos(5*sqrt(x)) + (2/25) * sin(5*sqrt(x)) + C

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