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

The integral of (6csc(x)cot(x)) is -6csc(x)+C

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integral of (6csc(x)cot(x))

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

- 6 csc (x) + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

: \int - 1 d u

= 6 \cdot \int - 1 d u

Integral of a constant:

\int a d x = a x

= 6 (- 1) u

Substitute back

u = csc (x)

= 6 (- 1) csc (x)

Simplify

= - 6 csc (x)

Add a constant to the solution

= - 6 csc (x) + C

x^{2} \cdot sin (x)

f (x) = 3 x^{2} - 2 x

- 9 x^{4}

\int sin (\frac{π x}{2}) d x

ln (x - x^{2})

What is the integral of (6csc(x)cot(x)) ?
The integral of (6csc(x)cot(x)) is -6csc(x)+C