簡約 ((2x+1)sin(x)-(x-1)(x+2)cos(x))sin(x)

解

簡約

((2 x + 1) sin (x) - (x - 1) (x + 2) cos (x)) sin (x)

(2 x sin (x) + sin (x) - x^{2} cos (x) - x cos (x) + 2 cos (x)) sin (x)

解答ステップ

((2 x + 1) sin (x) - (x - 1) (x + 2) cos (x)) sin (x)

= (sin (x) (2 x + 1) - cos (x) (x - 1) (x + 2)) sin (x)

拡張

sin (x) (2 x + 1) : 2 x sin (x) + sin (x)

= (2 x sin (x) + sin (x) - cos (x) (x - 1) (x + 2)) sin (x)

拡張

- cos (x) (x - 1) (x + 2) : - x^{2} cos (x) - x cos (x) + 2 cos (x)

= (2 x sin (x) + sin (x) - x^{2} cos (x) - x cos (x) + 2 cos (x)) sin (x)