What is the integral of cot(43x) ?

The integral of cot(43x) is 1/43 ln|sin(43x)|+C

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integral of cot(43x)

\int cot (43 x) d x

\frac{1}{43} ln ∣ sin (43 x) ∣ + C

Solution steps

\int cot (43 x) d x

Rewrite using trig identities

= \int \frac{cos ( 43 x )}{sin ( 43 x )} d x

Apply u-substitution

: \int \frac{1}{43 u} d u

= \int \frac{1}{43 u} d u

Take the constant out:

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

= \frac{1}{43} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{43} ln ∣ u ∣

Substitute back

u = sin (43 x)

= \frac{1}{43} ln ∣ sin (43 x) ∣

Add a constant to the solution

= \frac{1}{43} ln ∣ sin (43 x) ∣ + C

y = (3 x - 1)^{2}

n = 0 \sum \infty (1 - p)^{n}

\int 3 tan (2 x) d x

f (- 4) = - 5 x + 2

\frac{d y}{d x} = y + 1

What is the integral of cot(43x) ?
The integral of cot(43x) is 1/43 ln|sin(43x)|+C