What is the integral of (4cos(x)-6cos(2x)) ?

The integral of (4cos(x)-6cos(2x)) is 4sin(x)-3sin(2x)+C

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integral of (4cos(x)-6cos(2x))

\int (4 cos (x) - 6 cos (2 x)) d x

4 sin (x) - 3 sin (2 x) + C

Solution steps

\int 4 cos (x) - 6 cos (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 4 cos (x) d x - \int 6 cos (2 x) d x

\int 4 cos (x) d x = 4 sin (x)

\int 6 cos (2 x) d x = 3 sin (2 x)

= 4 sin (x) - 3 sin (2 x)

Add a constant to the solution

= 4 sin (x) - 3 sin (2 x) + C

\int 2 x sin (y) d x

\int (1 + cos (2 x))^{3} d x

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

\int sin (\frac{x}{6}) d x

\int (x - 3) (6 x + 4) d x

What is the integral of (4cos(x)-6cos(2x)) ?
The integral of (4cos(x)-6cos(2x)) is 4sin(x)-3sin(2x)+C