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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

arcsin (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 = arcsin (u)

= arcsin (u)

Substitute back

u = e^{t}

= arcsin (e^{t})

Add a constant to the solution

= arcsin (e^{t}) + C

n = 0 \sum \infty (- 1)^{n} (n + 1)

\int x e^{(- x)} d x

f (x) = e^{l n (x)} - e^{5 l n (x^{2})}

f (x) = tan (x) cot (x)

\frac{d}{d x} (\frac{3}{( x - 4 ) ^{2}})

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