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

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

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

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

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

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int e^{- x} d x = - e^{- x}

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

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

Simplify

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

Add a constant to the solution

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

\frac{d}{d x} ((x^{6} - 2)^{3})

2 y^{^{''}} - 6 y^{^{'}} + 4 y = 6 e^{2 t}

\int e^{2 x} (3 + e^{2 x})^{5} d x

\int_{- 1}^{2} \frac{5 x}{x ^{2} - x - 6} d x

y^{^{''}} + 3 y^{^{'}} + 2 y = 4

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