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

The integral of (sin(3x))/(3+3cos(3x)) is -1/9 ln|3+3cos(3x)|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (sin(3x))/(3+3cos(3x))

\int \frac{sin ( 3 x )}{3 + 3 cos ( 3 x )} d x

- \frac{1}{9} ln ∣ 3 + 3 cos (3 x) ∣ + C

Solution steps

\int \frac{sin ( 3 x )}{3 + 3 cos ( 3 x )} d x

Apply u-substitution

: \int - \frac{1}{9 u} d u

= \int - \frac{1}{9 u} d u

Take the constant out:

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

= - \frac{1}{9} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - \frac{1}{9} ln ∣ u ∣

Substitute back

u = 3 + 3 cos (3 x)

= - \frac{1}{9} ln ∣ 3 + 3 cos (3 x) ∣

Add a constant to the solution

= - \frac{1}{9} ln ∣ 3 + 3 cos (3 x) ∣ + C

\frac{d y}{d x}, 3 x y = 6

\int_{- 1}^{2} (x^{3}) d x

f (x) = 2 x + 1, 1, 5

\int sin (π)

What is the integral of (sin(3x))/(3+3cos(3x)) ?
The integral of (sin(3x))/(3+3cos(3x)) is -1/9 ln|3+3cos(3x)|+C