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

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

n = 0 \sum \infty \frac{( - 4 ) ^{3 n}}{5 ^{n - 1}}

\int [\frac{1}{( 4 + x ^{2} )}] d x

x \to - 5 lim (\frac{x + 4}{x + 5})

\int_{1}^{3} (x^{2} + 3)^{3} x d x

\frac{1}{( 1 - x )}, 0