What is the integral of (sin(x))/(e^{2x)} ?

The integral of (sin(x))/(e^{2x)} is -2/5 e^{-2x}sin(x)-1/5 e^{-2x}cos(x)+C

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integral of (sin(x))/(e^{2x)}

\int \frac{sin ( x )}{e ^{2 x}} d x

- \frac{2}{5} e^{- 2 x} sin (x) - \frac{1}{5} e^{- 2 x} cos (x) + C

Solution steps

\int \frac{sin ( x )}{e ^{2 x}} d x

Apply Integration By Parts

: - \frac{1}{2} e^{- 2 x} sin (x) - \int - \frac{1}{2} e^{- 2 x} cos (x) d x

= - \frac{1}{2} e^{- 2 x} sin (x) - \int - \frac{1}{2} e^{- 2 x} cos (x) d x

\int - \frac{1}{2} e^{- 2 x} cos (x) d x = - \frac{1}{10} (e^{- 2 x} sin (x) - 2 e^{- 2 x} cos (x))

= - \frac{1}{2} e^{- 2 x} sin (x) - (- \frac{1}{10} (e^{- 2 x} sin (x) - 2 e^{- 2 x} cos (x)))

Simplify

- \frac{1}{2} e^{- 2 x} sin (x) - (- \frac{1}{10} (e^{- 2 x} sin (x) - 2 e^{- 2 x} cos (x))) : - \frac{2}{5} e^{- 2 x} sin (x) - \frac{1}{5} e^{- 2 x} cos (x)

= - \frac{2}{5} e^{- 2 x} sin (x) - \frac{1}{5} e^{- 2 x} cos (x)

Add a constant to the solution

= - \frac{2}{5} e^{- 2 x} sin (x) - \frac{1}{5} e^{- 2 x} cos (x) + C

y^{^{'}} = \frac{x - 1}{y - 1}

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

\frac{- 3}{( s - 3 ) ^{2} + 4}

\int \frac{72 x}{( x - 7 ) ^{10}} d x

\int_{0}^{\infty} \frac{1}{1 + x ^{2}} d x

What is the integral of (sin(x))/(e^{2x)} ?
The integral of (sin(x))/(e^{2x)} is -2/5 e^{-2x}sin(x)-1/5 e^{-2x}cos(x)+C