What is the integral of 3cos(x)+1/x ?

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

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integral of 3cos(x)+1/x

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

3 sin (x) + ln ∣ x ∣ + C

Solution steps

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

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

\int \frac{1}{x} d x = ln ∣ x ∣

= 3 sin (x) + ln ∣ x ∣

Add a constant to the solution

= 3 sin (x) + ln ∣ x ∣ + C

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