What is the integral of (csc^2(t)-2e^t) ?

The integral of (csc^2(t)-2e^t) is -cot(t)-2e^t+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (csc^2(t)-2e^t)

\int (csc^{2} (t) - 2 e^{t}) d t

- cot (t) - 2 e^{t} + C

Solution steps

\int csc^{2} (t) - 2 e^{t} d t

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int csc^{2} (t) d t - \int 2 e^{t} d t

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

\int 2 e^{t} d t = 2 e^{t}

= - cot (t) - 2 e^{t}

Add a constant to the solution

= - cot (t) - 2 e^{t} + C

What is the integral of (csc^2(t)-2e^t) ?
The integral of (csc^2(t)-2e^t) is -cot(t)-2e^t+C