What is the integral of e^{-int} ?

The integral of e^{-int} is 1/n sin(nt)+i 1/n cos(nt)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of e^{-int}

\int e^{- in t} d t

\frac{1}{n} sin (n t) + i \frac{1}{n} cos (n t) + C

Solution steps

\int e^{- in t} d t

Simplify

e^{- in t} : cos (n t) - i sin (n t)

= \int cos (n t) - i sin (n 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 cos (n t) d t - \int i sin (n t) d t

\int cos (n t) d t = \frac{1}{n} sin (n t)

\int i sin (n t) d t = - i \frac{1}{n} cos (n t)

= \frac{1}{n} sin (n t) - (- i \frac{1}{n} cos (n t))

Simplify

\frac{1}{n} sin (n t) - (- i \frac{1}{n} cos (n t)) : \frac{1}{n} sin (n t) + i \frac{1}{n} cos (n t)

= \frac{1}{n} sin (n t) + i \frac{1}{n} cos (n t)

Add a constant to the solution

= \frac{1}{n} sin (n t) + i \frac{1}{n} cos (n t) + C

\int 9 x \cdot e^{3 x} d x

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

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

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

\int 5 x^{2} \cdot x d x

What is the integral of e^{-int} ?
The integral of e^{-int} is 1/n sin(nt)+i 1/n cos(nt)+C