展开 (1+2x^3)e^{x^2}

解答

展开

(1 + 2 x^{3}) e^{x^{2}}

e^{x^{2}} + 2 e^{x^{2}} x^{3}

求解步骤

(1 + 2 x^{3}) e^{x^{2}}

= e^{x^{2}} (1 + 2 x^{3})

使用分配律:

a (b + c) = ab + a c

a = e^{x^{2}}, b = 1, c = 2 x^{3}

= e^{x^{2}} \cdot 1 + e^{x^{2}} \cdot 2 x^{3}

= 1 \cdot e^{x^{2}} + 2 e^{x^{2}} x^{3}

乘以:

1 \cdot e^{x^{2}} = e^{x^{2}}

= e^{x^{2}} + 2 e^{x^{2}} x^{3}

e x p an d (x - \frac{2}{x})^{15}

e x p an d l im x \Rightarrow 1 (x^{3} + 3 x^{2} - x - 3) (x^{2} - 1)

s im pl i f y (z - \frac{1}{2}) (z - \frac{1}{3})

e x p an d sin (π (x + 1))

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