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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

arcsin (1 - e^{- 2 x}) + C

Solution steps

\int \frac{1}{e ^{x} 1 - e ^{- 2 x}} 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 = arcsin (u)

= arcsin (u)

Substitute back

u = 1 - e^{- 2 x}

= arcsin (1 - e^{- 2 x})

Add a constant to the solution

= arcsin (1 - e^{- 2 x}) + C

\int \frac{x}{( x + 2 ) ( 4 x - 1 )} d x

\frac{d}{d x} (x^{2.1})

\frac{d}{d x} (ln (\frac{a ^{2} - x ^{2}}{x}))

y (X) = - 3^{X}

x \to 3 lim (2 x^{2} + 1)

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