What is the integral of (1/2 1/x+4sin(x)) ?

The integral of (1/2 1/x+4sin(x)) is 1/2 ln|x|-4cos(x)+C

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integral of (1/2 1/x+4sin(x))

\int (\frac{1}{2} \frac{1}{x} + 4 sin (x)) d x

\frac{1}{2} ln ∣ x ∣ - 4 cos (x) + C

Solution steps

\int \frac{1}{2} \cdot \frac{1}{x} + 4 sin (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{1}{2} \cdot \frac{1}{x} d x + \int 4 sin (x) d x

\int \frac{1}{2} \cdot \frac{1}{x} d x = \frac{1}{2} ln ∣ x ∣

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

= \frac{1}{2} ln ∣ x ∣ - 4 cos (x)

Add a constant to the solution

= \frac{1}{2} ln ∣ x ∣ - 4 cos (x) + C

What is the integral of (1/2 1/x+4sin(x)) ?
The integral of (1/2 1/x+4sin(x)) is 1/2 ln|x|-4cos(x)+C