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Popular Calculus >

integral of e^{-it}

Solution

\int e^{- i t} d t

Solution

sin (t) + i cos (t) + C

Solution steps

\int e^{- i t} d t

Simplify

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

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

\int cos (t) d t = sin (t)

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

= sin (t) - (- i cos (t))

Simplify

= sin (t) + i cos (t)

Add a constant to the solution

= sin (t) + i cos (t) + C

Popular Examples

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integral of ((u+1))/(u(u+2))

integral of (9x)/(1+x^2)

integral of (2x^3+x-1)/(x^2-5x)

integral of e^{5x}

Frequently Asked Questions (FAQ)

What is the integral of e^{-it} ?
The integral of e^{-it} is sin(t)+icos(t)+C