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{\partial}{\partial x} (\frac{x}{y + z})

\int x sin (4 x^{2}) d x

x \to - 2 lim (4 - 2 x)

\frac{\partial}{\partial x} ((3 x - x^{2}) y e^{- y})

x \to 0 lim (x^{2} cos (\frac{7}{x}))

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