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

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

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

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

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

Solution steps

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

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

Add a constant to the solution

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

\frac{d y}{d x} + \frac{y}{x} = 3 x^{6} y^{2}

x \to 1 + lim (7)

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

7 z^{2} e^{z}

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

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