What is the integral of cot(42x) ?

The integral of cot(42x) is 1/42 ln|sin(42x)|+C

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integral of cot(42x)

\int cot (42 x) d x

\frac{1}{42} ln ∣ sin (42 x) ∣ + C

Solution steps

\int cot (42 x) d x

Rewrite using trig identities

= \int \frac{cos ( 42 x )}{sin ( 42 x )} d x

Apply u-substitution

: \int \frac{1}{42 u} d u

= \int \frac{1}{42 u} d u

Take the constant out:

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

= \frac{1}{42} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{42} ln ∣ u ∣

Substitute back

u = sin (42 x)

= \frac{1}{42} ln ∣ sin (42 x) ∣

Add a constant to the solution

= \frac{1}{42} ln ∣ sin (42 x) ∣ + C

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\frac{d}{d x} (3^{x^{3} - x + 1})

\frac{d}{d x} (arcsec (\frac{x}{a}))

\int_{- \infty}^{0} \frac{1}{5 - 8 x} d x

\frac{d}{d x} (x^{2} sec (\frac{1}{x ^{3}}))

What is the integral of cot(42x) ?
The integral of cot(42x) is 1/42 ln|sin(42x)|+C