gives us Step 3 15 sin x 1 sin x cos x dx 15 sin x cos x dx Since cos x is the derivative of sin x then S 15 sin x cos x dx can be done by substituting u sin x Step 4 With the substitution u sin x we get 15 0 15 which integrates to 15 sin x cos x dx 15 5u u du C 5u Substituting back in to get the answer in terms of sin x we have 15 sin x cos x dx 5 sin x 5 sin x C In terms of u we get Step 5 Using the same substitution u sin x enables us to do f 15 15 sin x cos x dx 15 5 04 S 15 sin x cos x u du C which in terms of sin x becomes C 15 sin r cos r dx sin x and du cos x cos x dx