What is the integral of (-2/x+3cos(6x)) ?

The integral of (-2/x+3cos(6x)) is -2ln|x|+1/2 sin(6x)+C

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integral of (-2/x+3cos(6x))

\int (- \frac{2}{x} + 3 cos (6 x)) d x

- 2 ln ∣ x ∣ + \frac{1}{2} sin (6 x) + C

Solution steps

\int - \frac{2}{x} + 3 cos (6 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 \frac{2}{x} d x + \int 3 cos (6 x) d x

\int \frac{2}{x} d x = 2 ln ∣ x ∣

\int 3 cos (6 x) d x = \frac{1}{2} sin (6 x)

= - 2 ln ∣ x ∣ + \frac{1}{2} sin (6 x)

Add a constant to the solution

= - 2 ln ∣ x ∣ + \frac{1}{2} sin (6 x) + C

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What is the integral of (-2/x+3cos(6x)) ?
The integral of (-2/x+3cos(6x)) is -2ln|x|+1/2 sin(6x)+C