What is the integral of 2cos(x)+5/x ?

The integral of 2cos(x)+5/x is 2sin(x)+5ln|x|+C

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integral of 2cos(x)+5/x

\int 2 cos (x) + \frac{5}{x} d x

2 sin (x) + 5 ln ∣ x ∣ + C

Solution steps

\int 2 cos (x) + \frac{5}{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 2 cos (x) d x + \int \frac{5}{x} d x

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

\int \frac{5}{x} d x = 5 ln ∣ x ∣

= 2 sin (x) + 5 ln ∣ x ∣

Add a constant to the solution

= 2 sin (x) + 5 ln ∣ x ∣ + C

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What is the integral of 2cos(x)+5/x ?
The integral of 2cos(x)+5/x is 2sin(x)+5ln|x|+C