What is the integral of cot(14x) ?

The integral of cot(14x) is 1/14 ln|sin(14x)|+C

Popular >

integral of cot(14x)

\int cot (14 x) d x

\frac{1}{14} ln ∣ sin (14 x) ∣ + C

Solution steps

\int cot (14 x) d x

Rewrite using trig identities

= \int \frac{cos ( 14 x )}{sin ( 14 x )} d x

Apply u-substitution

: \int \frac{1}{14 u} d u

= \int \frac{1}{14 u} d u

Take the constant out:

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

= \frac{1}{14} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{14} ln ∣ u ∣

Substitute back

u = sin (14 x)

= \frac{1}{14} ln ∣ sin (14 x) ∣

Add a constant to the solution

= \frac{1}{14} ln ∣ sin (14 x) ∣ + C

\int sec^{2} (2 y) d y

\frac{d}{d x} (4 (x + 2)^{\frac{3}{2}})

\frac{d y}{d t} = - \frac{y}{t} - 6

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

n = 1 \sum \infty \frac{1 ^{n}}{3 ^{n}}

What is the integral of cot(14x) ?
The integral of cot(14x) is 1/14 ln|sin(14x)|+C