What is the integral of (e^{2x})/((e^{2x)+1)^3} ?

The integral of (e^{2x})/((e^{2x)+1)^3} is -1/(4(e^{2x)+1)^2}+C

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integral of (e^{2x})/((e^{2x)+1)^3}

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

- \frac{1}{4 ( e ^{2 x} + 1 ) ^{2}} + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{2 u ^{3}} d u

= \int \frac{1}{2 u ^{3}} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int \frac{1}{u ^{3}} d u

Apply the Power Rule

: - \frac{1}{2 u ^{2}}

= \frac{1}{2} (- \frac{1}{2 u ^{2}})

Substitute back

u = e^{2 x} + 1

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

Simplify

\frac{1}{2} (- \frac{1}{2 ( e ^{2 x} + 1 ) ^{2}}) : - \frac{1}{4 ( e ^{2 x} + 1 ) ^{2}}

= - \frac{1}{4 ( e ^{2 x} + 1 ) ^{2}}

Add a constant to the solution

= - \frac{1}{4 ( e ^{2 x} + 1 ) ^{2}} + C

\frac{d}{d x} (lo g_{5} (sin^{2} (x)))

\int 441 - x^{2} d x

x \to 0 - lim (\frac{x + 1}{x ^{2}})

\int 17 sin^{3} (x co) s^{2} x d x

\frac{d y}{d x} = 1 0^{- 21} \cdot y^{3}

What is the integral of (e^{2x})/((e^{2x)+1)^3} ?
The integral of (e^{2x})/((e^{2x)+1)^3} is -1/(4(e^{2x)+1)^2}+C