展开 ((5(cos(x)-1)(e^2x-1)))/(3(e^x+1)x^3)

解答

展开

\frac{( 5 ( cos ( x ) - 1 ) ( e ^{2} x - 1 ) )}{3 ( e ^{x} + 1 ) x ^{3}}

\frac{5 e ^{2} x cos ( x ) - 5 cos ( x ) - 5 e ^{2} x + 5}{3 e ^{x} x ^{3} + 3 x ^{3}}

求解步骤

\frac{5 ( cos ( x ) - 1 ) ( e ^{2} x - 1 )}{3 ( e ^{x} + 1 ) x ^{3}}

乘开

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

= \frac{5 ( cos ( x ) - 1 ) ( e ^{2} x - 1 )}{3 e ^{x} x ^{3} + 3 x ^{3}}

乘开

5 (cos (x) - 1) (e^{2} x - 1) : 5 e^{2} x cos (x) - 5 cos (x) - 5 e^{2} x + 5

= \frac{5 e ^{2} x cos ( x ) - 5 cos ( x ) - 5 e ^{2} x + 5}{3 e ^{x} x ^{3} + 3 x ^{3}}

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

s im pl i f y (x + 2) \cdot (x + 3)

e x p an d r (t) (t cos (t) -, t) i + (t, t + cos (t)) j + t^{2} k

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

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