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

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

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

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

- 2 cos (x) - sin (x) + C

Solution steps

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

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

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

= - 2 cos (x) - sin (x)

Add a constant to the solution

= - 2 cos (x) - sin (x) + C

\frac{\partial}{\partial x} (\frac{x ^{2}}{2 y} + \frac{3 y ^{2}}{x ^{2}})

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

k = 0 \sum \infty \frac{x ^{k}}{k !}

- cos (x), cos^{2} (x), [\frac{- π}{2}, \frac{π}{2}]

\int 12 x d x

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