Step 1 x cos 8x dx To find the indefinite integral Let u 8zx The differential of u with respect to x is du 167 Step 2 Rewrite the integration in terms of u 1 Apply the constant multiplication rule on the right side 1 x cos 8x dx use the trigonometric identities x cos 8x dx cos U 16 Step 3 Integrate the right side 15 cos 16 cos u du 16 sin u 16 16T cos u du sin u C 16T 3 16 T du Step 4 Substitute the expression for u on the right side and obtain the integral 16 T x d