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

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

Popular >

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

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

cos (e^{- x}) + C

Solution steps

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

\int \frac{( ln ( u ) ) ^{6}}{u} d u

\int \frac{4 x - 3}{x ^{2} + 4 x + 20} d x

\int \frac{6}{1 - x ^{2}} d x

\int (- x^{2} - 2 x + 3) d x

\int \frac{4}{9 x ^{2} - 6 x} d x

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