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

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

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

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

arcsin (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 = arcsin (u)

= arcsin (u)

Substitute back

u = e^{x}

= arcsin (e^{x})

Add a constant to the solution

= arcsin (e^{x}) + C

\int x - 1 d x

\int_{1}^{2} x x - 1 d x

\frac{1}{s ^{2} ( s + \frac{1}{15} )}

\frac{d}{d x} (a x^{4})

n = 1 \sum \infty n^{2} (\frac{5}{6})^{n}

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