What is the integral of (e^x)/((e^x+2)^2) ?

The integral of (e^x)/((e^x+2)^2) is -1/(e^x+2)+C

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integral of (e^x)/((e^x+2)^2)

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

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

Solution steps

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

Apply u-substitution

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

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

Apply the Power Rule

: - \frac{1}{u}

= - \frac{1}{u}

Substitute back

u = e^{x} + 2

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

Add a constant to the solution

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

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