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Popular >

integral of (cos(x))/(2-sin(x))

Solution

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

Solution

- ln ∣ 2 - sin (x) ∣ + C

Solution steps

\int \frac{cos ( x )}{2 - sin ( 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 = 2 - sin (x)

= - ln ∣ 2 - sin (x) ∣

Add a constant to the solution

= - ln ∣ 2 - sin (x) ∣ + C

Popular Examples

y^{''}+4y^'+3y=sqrt(x)

y^{^{''}} + 4 y^{^{'}} + 3 y = x

derivative of 3/(2-2x^2)derivative of

\frac{3}{2 - 2 x ^{2}}

integral of (x^2)/(25+x^2)

\int \frac{x ^{2}}{25 + x ^{2}} d x

derivative of 3\sqrt[3]{x^4}

(\partial)/(\partial x)(4y(1/x-ln(x)))

\frac{\partial}{\partial x} (4 y (\frac{1}{x} - ln (x)))

Frequently Asked Questions (FAQ)

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