Step 4 With the substitution u sin x we get 15 sin x cos x dx 15 S which integrates to 13 5u 573 u du G Substituting back in to get the answer in terms of sin x we have sin x In terms of u we get 3u 15 sin x cos x dx 5 sin Step 5 Using the same substitution u sin x enables us to do 15 sin x cos x dx 15 Step 6 Combining these results we have J 15 sin x cos x dx 5 u du 3u 5 sin a C sin x C which in terms of sin x becomes 3 sin x 3 sin x C sin r and du cos x cos x dx