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

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

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

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

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

Solution steps

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

Factor

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

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

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

Add a constant to the solution

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

\int \frac{3}{y ^{3}} d y

f (x) = x^{2} - 4, at 5

\int x sin (x) d x

ln (1)

x \to \infty lim (\frac{11}{2})

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