What is the integral of (cot(x)) ?

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

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integral of (cot(x))

\int (cot (x)) d x

ln ∣ sin (x) ∣ + C

Solution steps

\int cot (x) d x

Rewrite using trig identities

= \int \frac{cos ( x )}{sin ( x )} d x

Apply u-substitution

: \int \frac{1}{u} d u

= \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = sin (x)

= ln ∣ sin (x) ∣

Add a constant to the solution

= ln ∣ sin (x) ∣ + C

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

3 x + 7

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\int 10 x + 11 d x

\int x^{2} 8 x^{3} + 1 d x