What is the integral of (5e^x)/(sqrt(1-e^{2x))} ?

The integral of (5e^x)/(sqrt(1-e^{2x))} is 5arcsin(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 (5e^x)/(sqrt(1-e^{2x))}

\int \frac{5 e ^{x}}{1 - e ^{2 x}} d x

5 arcsin (e^{x}) + C

Solution steps

\int \frac{5 e ^{x}}{1 - e ^{2 x}} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 5 \cdot \int \frac{e ^{x}}{1 - e ^{2 x}} d x

Apply u-substitution

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

= 5 \cdot \int \frac{1}{1 - u ^{2}} d u

Use the common integral:

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

= 5 arcsin (u)

Substitute back

u = e^{x}

= 5 arcsin (e^{x})

Add a constant to the solution

= 5 arcsin (e^{x}) + C

\int 14 tan^{13} (x) sec^{2} (x) d x

\int + 7 sin (\frac{θ}{3}) d θ

\int - 6 sin (x) e^{x} d x

\int cos (2 t) (e^{6 t}) d t

\int \frac{5 x ^{4}}{x ^{5} + 2} d x

What is the integral of (5e^x)/(sqrt(1-e^{2x))} ?
The integral of (5e^x)/(sqrt(1-e^{2x))} is 5arcsin(e^x)+C