What is the integral of (1/x-sin(x)) ?

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

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integral of (1/x-sin(x))

\int (\frac{1}{x} - sin (x)) d x

ln ∣ x ∣ + cos (x) + C

Solution steps

\int \frac{1}{x} - 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}{x} d x - \int sin (x) d x

\int \frac{1}{x} d x = ln ∣ x ∣

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

= ln ∣ x ∣ - (- cos (x))

Simplify

= ln ∣ x ∣ + cos (x)

Add a constant to the solution

= ln ∣ x ∣ + cos (x) + C

\int (8 + \frac{2}{5} x^{2} + \frac{3}{7} x^{3}) d x

\int 17 x sin (17 x^{2}) d x

\int \frac{ln ( 2 x )}{ln ( 4 x )} d x

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

\int \frac{1}{e ^{n}}

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