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

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

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

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

- 2 ln ∣ sin (x) ∣ + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

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

= - 2 \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - 2 ln ∣ u ∣

Substitute back

u = sin (x)

= - 2 ln ∣ sin (x) ∣

Add a constant to the solution

= - 2 ln ∣ sin (x) ∣ + C

x \to 5 + lim (\frac{6}{x - 5})

x \to 0 lim (x^{3} cos (\frac{6}{x}))

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

\int 3 x^{\frac{1}{2}} d x

y = x^{3} + 3 x^{2} + 2

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