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)

Add a constant to the solution

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

\int_{0}^{3} cos (\frac{n x π}{3}) d x

\frac{d}{d x} (\frac{x - 1}{x + 2})

\frac{\partial}{\partial x} (\frac{x}{4} + y)

\frac{\partial}{\partial x} (b)

\frac{d}{d x} (x l)

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