What is expand (dx)/((e^x+1)^3e^{-x)} ?

The solution to expand (dx)/((e^x+1)^3e^{-x)} is (dx)/(e^{2x)+3e^x+3+e^{-x}}

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expand (dx)/((e^x+1)^3e^{-x)}

expand

\frac{d x}{( e ^{x} + 1 ) ^{3} e ^{- x}}

\frac{d x}{e ^{2 x} + 3 e ^{x} + 3 + e ^{- x}}

Solution steps

\frac{d x}{( e ^{x} + 1 ) ^{3} e ^{- x}}

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

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

Expand

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

= \frac{d x}{e ^{2 x} + 3 e ^{x} + 3 + e ^{- x}}

\frac{[ x y ( 3 x ^{2} - 5 y ^{2} ) - x ^{4} + 3 y ^{4} ]}{( x - y ) ^{2}}

(2 x^{2} + 3 ux + ux) d x

(z - π)^{2}

\frac{2 t - 5 t ^{2}}{( 0.4 + t ^{2} ) ^{2}}

(1 - e - a t) sin (x)

What is expand (dx)/((e^x+1)^3e^{-x)} ?
The solution to expand (dx)/((e^x+1)^3e^{-x)} is (dx)/(e^{2x)+3e^x+3+e^{-x}}