What is the integral of (sin(4e^{-7x}))/(e^{7x)} ?

The integral of (sin(4e^{-7x}))/(e^{7x)} is 1/28 cos(4e^{-7x})+C

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integral of (sin(4e^{-7x}))/(e^{7x)}

\int \frac{sin ( 4 e ^{- 7 x} )}{e ^{7 x}} d x

\frac{1}{28} cos (4 e^{- 7 x}) + C

Solution steps

\int \frac{sin ( 4 e ^{- 7 x} )}{e ^{7 x}} d x

Apply u-substitution

: \int - \frac{sin ( u )}{28} d u

= \int - \frac{sin ( u )}{28} d u

Take the constant out:

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

= - \frac{1}{28} \cdot \int sin (u) d u

Use the common integral:

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

= - \frac{1}{28} (- cos (u))

Substitute back

u = 4 e^{- 7 x}

= - \frac{1}{28} (- cos (4 e^{- 7 x}))

Simplify

= \frac{1}{28} cos (4 e^{- 7 x})

Add a constant to the solution

= \frac{1}{28} cos (4 e^{- 7 x}) + C

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What is the integral of (sin(4e^{-7x}))/(e^{7x)} ?
The integral of (sin(4e^{-7x}))/(e^{7x)} is 1/28 cos(4e^{-7x})+C