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

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

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

ln ∣ 6 + sin (x) ∣ + C

Solution steps

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

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 = 6 + sin (x)

= ln ∣ 6 + sin (x) ∣

Add a constant to the solution

= ln ∣ 6 + sin (x) ∣ + C

\frac{6}{s ( s + 4 )}

\frac{d}{d x} (a x^{2} + b x + c)

(x^{2} + 1) \frac{d y}{d x} + 2 x y = 4 x^{2}

\int 10 sin^{2} (x co) s^{2} x d x

\frac{d}{d x} (k x^{4} (x_{0} - x))

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