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

= \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

\frac{d ^{2}}{d x ^{2}} (sin (5) x^{5})

(1.3) (3.5)

\frac{d}{d x} ((2 x - 7)^{3})

f (x) = \frac{x}{x + 1}, (- 2, 2)

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

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