Use a combination of substitution and parts to evaluate the integral sin(7√x)dx: Step 1: Substitution, let w = 7√. 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 dw = 27 dz -dx and dx = 2√x dx = f(w)dw, where f(w) = Complete the substitution, to get 2√ -dw. To successfully continue with substitution, it is now necessary to rewrite da strictly in terms of w. Thus 7 [sin(7√)dx = [9(w)dw where g(w) : = Step 2: Use integration by parts to integrate g(w)dw. Let u = [ Step 3: Substitute 7√ for w, to get sin(7√)dx=+C. -0 +9(w)dw=+c. and du = sin (w)dw. This gives (as a function of w),

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