展开 (9+5cos^2(0.4x))*(5e^{-0.5x}+2e^{0.15x})

解答

展开

(9 + 5 cos^{2} (0.4 x)) \cdot (5 e^{- 0.5 x} + 2 e^{0.15 x})

45 e^{- 0.5 x} + 18 e^{0.15 x} + 25 e^{- 0.5 x} cos^{2} (0.4 x) + 10 e^{0.15 x} cos^{2} (0.4 x)

求解步骤

(9 + 5 cos^{2} (0.4 x)) (5 e^{- 0.5 x} + 2 e^{0.15 x})

使用 FOIL 方法:

(a + b) (c + d) = a c + a d + b c + b d

a = 9, b = 5 cos^{2} (0.4 x), c = 5 e^{- 0.5 x}, d = 2 e^{0.15 x}

= 9 \cdot 5 e^{- 0.5 x} + 9 \cdot 2 e^{0.15 x} + 5 cos^{2} (0.4 x) \cdot 5 e^{- 0.5 x} + 5 cos^{2} (0.4 x) \cdot 2 e^{0.15 x}

= 9 \cdot 5 e^{- 0.5 x} + 9 \cdot 2 e^{0.15 x} + 5 \cdot 5 e^{- 0.5 x} cos^{2} (0.4 x) + 5 \cdot 2 e^{0.15 x} cos^{2} (0.4 x)

化简

9 \cdot 5 e^{- 0.5 x} + 9 \cdot 2 e^{0.15 x} + 5 \cdot 5 e^{- 0.5 x} cos^{2} (0.4 x) + 5 \cdot 2 e^{0.15 x} cos^{2} (0.4 x) : 45 e^{- 0.5 x} + 18 e^{0.15 x} + 25 e^{- 0.5 x} cos^{2} (0.4 x) + 10 e^{0.15 x} cos^{2} (0.4 x)

= 45 e^{- 0.5 x} + 18 e^{0.15 x} + 25 e^{- 0.5 x} cos^{2} (0.4 x) + 10 e^{0.15 x} cos^{2} (0.4 x)

e x p an d \frac{( x ^{4} + 3 ) ^{3}}{12}

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

e x p an d 2 (e^{s i n (\frac{x}{4})} - 1)

e x p an d x (3 x + 5 vx) (v + x \frac{d v}{d x})

e x p an d (5 e^{3} + 3 p^{2})^{6}