What is the integral of (3cos(t))/(sin(t)) ?

The integral of (3cos(t))/(sin(t)) is 3ln|sin(t)|+C

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integral of (3cos(t))/(sin(t))

\int \frac{3 cos ( t )}{sin ( t )} d t

3 ln ∣ sin (t) ∣ + C

Solution steps

\int \frac{3 cos ( t )}{sin ( t )} d t

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int \frac{cos ( t )}{sin ( t )} d t

Apply u-substitution

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

= 3 \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 3 ln ∣ u ∣

Substitute back

u = sin (t)

= 3 ln ∣ sin (t) ∣

Add a constant to the solution

= 3 ln ∣ sin (t) ∣ + C

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What is the integral of (3cos(t))/(sin(t)) ?
The integral of (3cos(t))/(sin(t)) is 3ln|sin(t)|+C