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

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

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

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

arctan (e^{x}) + C

Solution steps

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

Apply u-substitution

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

Use the common integral:

\int \frac{1}{u ^{2} + 1} 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))/(e^{2x)+1} ?
The integral of ((e^x))/(e^{2x)+1} is arctan(e^x)+C