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

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

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

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

arctan (e^{t}) + C

Solution steps

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

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^{t}

= arctan (e^{t})

Add a constant to the solution

= arctan (e^{t}) + C

x \to - 5 + lim (\frac{∣ x + 5 ∣}{x + 5})

\frac{d}{d x} (sin^{3} (2 x^{2}))

\int 4^{x} \cdot e^{2 x} d x

x \to 0 lim (x - 10 + 5 x)

\frac{d}{d x} (3 a^{5 x})

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