What is the integral of (sin(x))/(6+cos(x)) ?

The integral of (sin(x))/(6+cos(x)) is -ln|6+cos(x)|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (sin(x))/(6+cos(x))

\int \frac{sin ( x )}{6 + cos ( x )} d x

- ln ∣ 6 + cos (x) ∣ + C

Solution steps

\int \frac{sin ( x )}{6 + cos ( x )} d x

Apply u-substitution

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

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

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - ln ∣ u ∣

Substitute back

u = 6 + cos (x)

= - ln ∣ 6 + cos (x) ∣

Add a constant to the solution

= - ln ∣ 6 + cos (x) ∣ + C

\int \frac{x + 1}{( x ^{2} + 2 x ) ^{3}} d x

\int \frac{60}{x ^{2}} d x

\int cos (\frac{2 π x}{a}) d x

\int \frac{- 5 ln ( x )}{x} d x

\int sec (t) (3 sec (t) + 2 tan (t)) d t

What is the integral of (sin(x))/(6+cos(x)) ?
The integral of (sin(x))/(6+cos(x)) is -ln|6+cos(x)|+C