What is the integral of e^{-t}sqrt(9-e^{2t)} ?

The integral of e^{-t}sqrt(9-e^{2t)} is -e^{-t}sqrt(9-e^{2t)}-arcsin(1/3 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(9-e^{2t)}

\int e^{- t} 9 - e^{2 t} d t

- e^{- t} 9 - e^{2 t} - arcsin (\frac{1}{3} e^{t}) + C

Solution steps

\int e^{- t} 9 - e^{2 t} d t

Apply Integration By Parts

: - e^{- t} 9 - e^{2 t} - \int \frac{e ^{t}}{9 - e ^{2 t}} d t

= - e^{- t} 9 - e^{2 t} - \int \frac{e ^{t}}{9 - e ^{2 t}} d t

\int \frac{e ^{t}}{9 - e ^{2 t}} d t = arcsin (\frac{1}{3} e^{t})

= - e^{- t} 9 - e^{2 t} - arcsin (\frac{1}{3} e^{t})

Add a constant to the solution

= - e^{- t} 9 - e^{2 t} - arcsin (\frac{1}{3} e^{t}) + C

\int 16 x sin (x) cos (x) d x

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

\int (e^{2 y} - e^{- 2 y}) d y

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

What is the integral of e^{-t}sqrt(9-e^{2t)} ?
The integral of e^{-t}sqrt(9-e^{2t)} is -e^{-t}sqrt(9-e^{2t)}-arcsin(1/3 e^t)+C