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

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

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

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

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

Solution steps

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

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

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

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

Simplify

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

Add a constant to the solution

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

\frac{\partial}{\partial u} (u^{2} + v^{2})

\int \frac{8 x}{1 - 4 x ^{2}} d x

f (x) = e^{1 + 2 t a n (x)}, at x = \frac{π}{4}

t \cdot sin (k \cdot t)

3 x^{2} \frac{d y}{d x} = 2 x^{2} + y^{2}

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