What is the integral of cot(t) ?

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

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integral of cot(t)

\int cot (t) d t

ln ∣ sin (t) ∣ + C

Solution steps

\int cot (t) d t

Rewrite using trig identities

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

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 (t)

= ln ∣ sin (t) ∣

Add a constant to the solution

= ln ∣ sin (t) ∣ + C

x \to - 2 lim (\frac{1}{x + 2})

\int sec^{2} (1 - 4 x) d x

\frac{d y}{d x} = e^{x - y}, y (0) = ln (8)

x \to 0 lim ((1 + 6 x)^{\frac{3}{x}})

\frac{1}{s ^{3} + s}