What is the integral of (cos(2x))/(2+3sin(2x)) ?

The integral of (cos(2x))/(2+3sin(2x)) is 1/6 ln|2+3sin(2x)|+C

Popular >

integral of (cos(2x))/(2+3sin(2x))

\int \frac{cos ( 2 x )}{2 + 3 sin ( 2 x )} d x

\frac{1}{6} ln ∣ 2 + 3 sin (2 x) ∣ + C

Solution steps

\int \frac{cos ( 2 x )}{2 + 3 sin ( 2 x )} d x

Apply u-substitution

: \int \frac{1}{6 u} d u

= \int \frac{1}{6 u} d u

Take the constant out:

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

= \frac{1}{6} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{6} ln ∣ u ∣

Substitute back

u = 2 + 3 sin (2 x)

= \frac{1}{6} ln ∣ 2 + 3 sin (2 x) ∣

Add a constant to the solution

= \frac{1}{6} ln ∣ 2 + 3 sin (2 x) ∣ + C

\int 2 e^{t} + 3 sin (t) d t

\int x \cdot 1 + x d x

\int x 2 x^{2} - 3 d x

\int t cos^{2} (2 t) d t

\int e^{- x} (2 e^{- x} + 3)^{9} d x

What is the integral of (cos(2x))/(2+3sin(2x)) ?
The integral of (cos(2x))/(2+3sin(2x)) is 1/6 ln|2+3sin(2x)|+C