What is the integral of 1/(tan(v)) ?

The integral of 1/(tan(v)) is ln|sin(v)|+C

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integral of 1/(tan(v))

\int \frac{1}{tan ( v )} d v

ln ∣ sin (v) ∣ + C

Solution steps

\int \frac{1}{tan ( v )} d v

Rewrite using trig identities

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

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 (v)

= ln ∣ sin (v) ∣

Add a constant to the solution

= ln ∣ sin (v) ∣ + C

\int_{0}^{8} \frac{1}{8 - x} d x

x^{2} arctan (3 x)

\frac{\partial}{\partial x} (e^{x - 1} cos (y))

\frac{d}{d x} (cos^{4} (sin^{3} (x)))

y = arccos (5 x)