What is the integral of (e^{2x})/(4+e^{2x)} ?

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

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integral of (e^{2x})/(4+e^{2x)}

\int \frac{e ^{2 x}}{4 + e ^{2 x}} d x

\frac{1}{2} ln 4 + e^{2 x} + C

Solution steps

\int \frac{e ^{2 x}}{4 + e ^{2 x}} d x

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{2} ln ∣ u ∣

Substitute back

u = 4 + e^{2 x}

= \frac{1}{2} ln 4 + e^{2 x}

Add a constant to the solution

= \frac{1}{2} ln 4 + e^{2 x} + C

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

\int tan (9 x) sec^{\frac{5}{4}} (9 x) d x

x \to \infty lim (x^{2} - 5)

t \to - 3 lim (\frac{t - 2}{t + 5})

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

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