展开 x(x^3e^{5x}+5)

解答

展开

x (x^{3} e^{5 x} + 5)

e^{5 x} x^{4} + 5 x

求解步骤

x (x^{3} e^{5 x} + 5)

= x (e^{5 x} x^{3} + 5)

使用分配律:

a (b + c) = ab + a c

a = x, b = x^{3} e^{5 x}, c = 5

= x x^{3} e^{5 x} + x \cdot 5

= e^{5 x} x^{3} x + 5 x

e^{5 x} x^{3} x = e^{5 x} x^{4}

= e^{5 x} x^{4} + 5 x

e x p an d lo g_{10} (a^{3} b)

e x p an d (x + Δ x - 2) (x - 2) \cdot (x - 2 + x + Δ x - 2)

e x p an d (- 1, - 1 + π) (x - 0, y + \frac{π}{2})

s im pl i f y (u + i v)^{3}

e x p an d \frac{1}{1 - 4 x}