What is the integral of sin(e^{-x}) ?

The integral of sin(e^{-x}) is -\Si(e^{-x})+C

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integral of sin(e^{-x})

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

- Si (e^{- x}) + C

Solution steps

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

Apply u-substitution

: \int - sin (e^{u}) d u

= \int - sin (e^{u}) d u

Take the constant out:

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

= - \int sin (e^{u}) d u

Apply u-substitution

: \int \frac{sin ( v )}{v} d v

= - \int \frac{sin ( v )}{v} d v

Use the nonelementary integral:

\int \frac{sin ( x )}{x} d x = Si (x)

= - Si (v)

Substitute back

= - Si (e^{- x})

Add a constant to the solution

= - Si (e^{- x}) + C

\frac{\partial}{\partial x} (2 x^{2} + y^{2} - 5 y)

e^{- 2 x} x^{3} (- x + 2)

\int t^{7} e^{- t^{8}} d t

x \to 2 lim (\frac{x}{2 - x})

\frac{d}{d t} (1 - cos (t))

What is the integral of sin(e^{-x}) ?
The integral of sin(e^{-x}) is -\Si(e^{-x})+C