October 19, 2017 2 x 2 6 x sin 3 2 2 x sin x 3 x dx x sin x x
the problem
1 cos x 2 6 x x sin x 3 2 2 x dx 3 x sin x x
3 x 2 1 cos x x sin x 3 2 3 x dx x x sin x
sin 2 u 2 =1-cos u 2
simplify
3 x 2 3 x 2 cos x x sin x 3 2 3 x dx x x sin x
ab+c =ab+ac
3 x 2 3 x 2 cos x x sin x 3 2 3 x dx x sin x 1 2 x
x = x 1 2
x sin x 1 2 3 x 2 3 x 2 cos x 3 2 3 x 1 2 x sin x d x 1 2 x ab+c =ab+ac
x sin x 1 2 3 x 2 3 x 2 cos x 1 2 x x 3 2 d x d x 3 x sin 1 2 x simplify
3 x sin x 1 2 x 2 3 x sin x 1 2 x 2 cos x 3 2 1 2 d x 3 x x sin x dx 1 2 x ab+c =ab+ac x x 1 2 x 3 2 d x x x 1 2 x 3 2 x d x x 1 2 x x 3 2 d x 3 sin 3 sin cos 3 sin simplify
October 19, 2017 1 2 2 1 2 3 2 3 2 1 2 2 4 dx 32 u sin u u du 3 x sin x x cos x dx 3 x x sin x
u = x 1 2 1 2 2 1 2 3 2 3 2 1 2 2 4 dx 32 u sin u u du 3 x sin x x cos x dx 3 x x sin x cu dt = c u dt 1 2 2 1 2 3 2 3 2 2 4 1 2 u du 3 x sin x x x sin x dx 6 u sin u cos x dx 3 x
arithmetic 1 2 1 2 2 2 3 2 2 4 2 4 2 1 2 u du 3 2 v v cos v dv 3 x x sin x dx 6 u sin u sin v
v = x 1 2
1 2 1 2 2 2 3 2 1 2 2 4 2 4 2 dx 6 u sin u u du 6 v sin v v cos v dv 3 x x sin x
simplify 1 2 1 2 2 2 2 4 2 4 2 6 u sin u u du 6 v sin v v cos v dv + 3 2 2 2 2 w dw 32 w sin w
w = x 1 2 1 2 1 2 2 2 2 4 2 4 2 6 u sin u u du 6 v sin v v cos v dv + 3 2 2 2 2 w dw 6 w sin w