With the substitution u sin x we get J which integrates to

Last updated: 7/4/2023

With the substitution u sin x we get J which integrates to 12 sin x cos x dx 12 u du Substituting back in to get the answer in terms of sin x we have I 12 sin x cos x dx 4 sin x 4 sin r C 12 sin 4u Step 5 Using the same substitution u sin x enables us to do 12 u dur 12 sin x cos x dx 12 In terms of u we get 12 C Step 6 Combining these results we have 12 sin x cos x dx 125 5 C which in terms of sin x becomes 12 sin r 5 C