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

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

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

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

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

Solution steps

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

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

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

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

Simplify

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

Add a constant to the solution

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

\frac{d}{d x} (2 a x - \frac{1}{x ^{2}})

\int \frac{5 x}{x ^{2}} d x

x^{3} - 4 x^{2} + 3 x, 0

(y + x) y^{^{'}} = y

\int_{0}^{π} x cos (2 x) d x

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