What is the integral of 6xcsc(6x)cot(6x) ?

The integral of 6xcsc(6x)cot(6x) is -xcsc(6x)+1/6 ln|tan(3x)|+C

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integral of 6xcsc(6x)cot(6x)

\int 6 x csc (6 x) cot (6 x) d x

- x csc (6 x) + \frac{1}{6} ln ∣ tan (3 x) ∣ + C

Solution steps

\int 6 x csc (6 x) cot (6 x) d x

Take the constant out:

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

= 6 \cdot \int x csc (6 x) cot (6 x) d x

Apply Integration By Parts

: - \frac{1}{6} x csc (6 x) - \int - \frac{1}{6} csc (6 x) d x

= 6 (- \frac{1}{6} x csc (6 x) - \int - \frac{1}{6} csc (6 x) d x)

\int - \frac{1}{6} csc (6 x) d x = - \frac{1}{36} ln ∣ tan (3 x) ∣

= 6 (- \frac{1}{6} x csc (6 x) - (- \frac{1}{36} ln ∣ tan (3 x) ∣))

Simplify

6 (- \frac{1}{6} x csc (6 x) - (- \frac{1}{36} ln ∣ tan (3 x) ∣)) : - x csc (6 x) + \frac{1}{6} ln ∣ tan (3 x) ∣

= - x csc (6 x) + \frac{1}{6} ln ∣ tan (3 x) ∣

Add a constant to the solution

= - x csc (6 x) + \frac{1}{6} ln ∣ tan (3 x) ∣ + C

f (x) = \frac{64}{x ^{2} + 16}, at x = - 4

5 e^{- t}

\frac{d}{d x} (arcsin (x))

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

y = x^{2} - 2 x, at x = 0

What is the integral of 6xcsc(6x)cot(6x) ?
The integral of 6xcsc(6x)cot(6x) is -xcsc(6x)+1/6 ln|tan(3x)|+C