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

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

- \frac{1 - e ^{2 x}}{e ^{x}} + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{u ^{2} 1 - u ^{2}} d u

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

Apply Trigonometric Substitution

: \int \frac{cot ( v )}{cos ( v ) sin ( v )} d v

= \int \frac{cot ( v )}{cos ( v ) sin ( v )} d v

Simplify

\frac{cot ( v )}{cos ( v ) sin ( v )} : csc^{2} (v)

= \int csc^{2} (v) d v

Use the common integral:

\int csc^{2} (v) d v = - cot (v)

= - cot (v)

Substitute back

= - cot (arcsin (e^{x}))

Simplify

- cot (arcsin (e^{x})) : - \frac{1 - e ^{2 x}}{e ^{x}}

= - \frac{1 - e ^{2 x}}{e ^{x}}

Add a constant to the solution

= - \frac{1 - e ^{2 x}}{e ^{x}} + C

f (x) = sin^{2} (\frac{x}{2})

x \cdot \frac{d y}{d x} + (11 + x) y = e^{- x}

\int_{0}^{x^{2}} sin (t) d t

\frac{d}{d x} (\frac{x ^{\frac{3}{2}}}{3} - x^{\frac{1}{2}})

\frac{7}{r ^{3}}

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