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

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

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

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

arctan (e^{x}) + C

Solution steps

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

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{1 + u ^{2}} d u = arctan (u)

= arctan (u)

Substitute back

u = e^{x}

= arctan (e^{x})

Add a constant to the solution

= arctan (e^{x}) + C

\frac{d}{d θ} (4 sin (θ))

\int \frac{1}{4 - x} d x

x \to 1 lim (x^{\frac{6}{1 - x}})

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

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