What is the integral of 2cot(x) ?

The integral of 2cot(x) is 2ln|sin(x)|+C

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integral of 2cot(x)

\int 2 cot (x) d x

2 ln ∣ sin (x) ∣ + C

Solution steps

\int 2 cot (x) d x

Take the constant out:

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

= 2 \cdot \int cot (x) d x

Rewrite using trig identities

= 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

\frac{d}{d x} (\frac{x y}{( x ^{2} - y ^{2} ) ^{2}})

x \to - 2 + lim (\frac{1}{x ^{2} - 4})

f (x) = x + 8, (1, 3)

n = 1 \sum \infty 3^{n} 5^{1 - n}

x \to \infty lim (\frac{x ^{\frac{1}{2}}}{x ^{\frac{2}{3}}})