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

解答

化简

((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)

求解步骤

((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)

展开

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)

展开

- 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)

e x p an d \frac{1}{( s + 1 ) ( s ^{3} + 3 s ^{2} + 3 s + 1 )}

e x p an d e^{x} (1 - 3 e^{- 2 x})

e x p an d \frac{4 ( 1 - 9 x ^{2} )}{( 1 + 3 x ^{2} ) ^{3}}

e x p an d cos^{2} (x) (1 - cos^{4} (x))

e x p an d \frac{1 + 4 x}{4 ( x + 1 )}