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

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

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integral of (1/x+cot(x))

\int (\frac{1}{x} + cot (x)) d x

ln ∣ x ∣ + ln ∣ sin (x) ∣ + C

Solution steps

\int \frac{1}{x} + cot (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 cot (x) d x

\int \frac{1}{x} d x = ln ∣ x ∣

\int cot (x) d x = ln ∣ sin (x) ∣

= ln ∣ x ∣ + ln ∣ sin (x) ∣

Add a constant to the solution

= ln ∣ x ∣ + ln ∣ sin (x) ∣ + C

\int \frac{5}{x ^{2} - 4 x + 8} d x

8^{t}

x \to 2 lim (9)

(1, 0.5), (3, 0)

\int x^{2} - 64 d x

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