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

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

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

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

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

Solution steps

\int \frac{e ^{2 x}}{2 + 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 = 2 + e^{2 x}

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

Add a constant to the solution

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

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

\int x^{2} + 2 y d y

\int 5 sec^{6} (t) d t

y = - x^{2} + 5 x + 2

x y^{^{''}} + 3 y^{^{'}} = 1984 x^{1982}

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