展开 x(x^3e^{5x}+2)

解答

展开

x (x^{3} e^{5 x} + 2)

e^{5 x} x^{4} + 2 x

求解步骤

x (x^{3} e^{5 x} + 2)

= x (e^{5 x} x^{3} + 2)

使用分配律:

a (b + c) = ab + a c

a = x, b = x^{3} e^{5 x}, c = 2

= x x^{3} e^{5 x} + x \cdot 2

= e^{5 x} x^{3} x + 2 x

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

= e^{5 x} x^{4} + 2 x

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

e x p an d 3 (x + 1) - 5 ln ∣ x + 1 ∣ + C

e x p an d \frac{( 2 n + 1 ) ( n + 1 ) n}{6}

e x p an d \frac{1}{( s + 1 ) ( s ^{2} + 4 s + 25 )}

e x p an d \frac{1}{5 ( 35 - 10 x )}