What is the integral of (cos(t))/(sin(t)) ?

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

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integral of (cos(t))/(sin(t))

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

ln ∣ sin (t) ∣ + C

Solution steps

\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^{2} \frac{d y}{d x} + x (x + 2) = e^{x}

n \to 0 lim (\frac{( ( 3 ) ^{n} - 1 )}{n})

x \to 0 + lim (ln (1 - cos (x)) - ln (sin (x)))

\frac{d}{d x} (18 x)

\frac{d y}{d t} + 2 y = 1, y (0) = \frac{5}{2}

What is the integral of (cos(t))/(sin(t)) ?
The integral of (cos(t))/(sin(t)) is ln|sin(t)|+C