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

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

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