What is the integral of sin(2x)-cos(x) ?

The integral of sin(2x)-cos(x) is -1/2 cos(2x)-sin(x)+C

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integral of sin(2x)-cos(x)

\int sin (2 x) - cos (x) d x

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

Solution steps

\int sin (2 x) - cos (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 sin (2 x) d x - \int cos (x) d x

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

\int cos (x) d x = sin (x)

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

Add a constant to the solution

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

\int_{0}^{2} x^{4} d x

x y^{^{'}} - 4 y^{2} = x^{2}

\frac{d}{d x} (\frac{3 x - 2}{2 x + 1})

f (x) = - \frac{1}{x + 2}, at x = 3

\frac{\partial}{\partial x} (e^{x} cos (x))

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