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

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

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integral of e^{-x}sin(e^{-x})

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

cos (e^{- x}) + C

Solution steps

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

Apply u-substitution

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

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

Take the constant out:

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

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

Apply u-substitution

: \int sin (v) d v

= - \int sin (v) d v

Use the common integral:

\int sin (v) d v = - cos (v)

= - (- cos (v))

Substitute back

= - (- cos (e^{- x}))

Simplify

= cos (e^{- x})

Add a constant to the solution

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

y = x (x + 11)

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

\frac{15}{ln ( x )}

\int r^{4} d r

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

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