What is the integral of-3cot(x) ?

The integral of-3cot(x) is -3ln|sin(x)|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of-3cot(x)

\int - 3 cot (x) d x

- 3 ln ∣ sin (x) ∣ + C

Solution steps

\int - 3 cot (x) d x

Take the constant out:

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

= - 3 \cdot \int cot (x) d x

Rewrite using trig identities

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

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 (x)

= - 3 ln ∣ sin (x) ∣

Add a constant to the solution

= - 3 ln ∣ sin (x) ∣ + C

\frac{d}{d x} (cos (x) ln (tan (x)))

(- 2, - 2), (2, - 5)

\int (x + 1) 2 - x d x

7 sin (x), \frac{π}{4}

x d y - y d x + (y^{2} - 1) d y = 0