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

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

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integral of (sin(x))/(e^x)

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

\int \frac{1}{x 12 x + 25} d x

x \to 0 - lim (- x)

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

(1, 1), (- 4, - 3)

y^{^{'}} = - 4 x y^{3}

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