cos( sin 8x 8 Also, u = x. Therefore, the differential is du = dx dr Step 2 To find the integral J x cos 8x dx by the parts formula, use u = x and v = Apply the rule of integration by parts. Judv 1 dv = uv - -11 du U Step 3 Substitute the expressions for u and v in the integral. √x cos x cos 8x dx = ( sin( J») -/ Apply the constant multiplication rule to integrate the right side and simplify. x cos 8x dx = sin 8x - (cos 8x) + C COS 8 1 sin 8x + V 8 x) dx 8 S cos 8x + C 18 sin 8x, as used in the previous step. x) dx sin(

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