What is the integral of tan(8x)sin(8x)cot(8x) ?

The integral of tan(8x)sin(8x)cot(8x) is -1/8 cos(8x)+C

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integral of tan(8x)sin(8x)cot(8x)

\int tan (8 x) sin (8 x) cot (8 x) d x

- \frac{1}{8} cos (8 x) + C

Solution steps

\int tan (8 x) sin (8 x) cot (8 x) d x

Rewrite using trig identities

= \int sin (8 x) d x

Apply u-substitution

: \int sin (u) \frac{1}{8} d u

= \int sin (u) \frac{1}{8} d u

Take the constant out:

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

= \frac{1}{8} \cdot \int sin (u) d u

Use the common integral:

\int sin (u) d u = - cos (u)

= \frac{1}{8} (- cos (u))

Substitute back

u = 8 x

= \frac{1}{8} (- cos (8 x))

Simplify

= - \frac{1}{8} cos (8 x)

Add a constant to the solution

= - \frac{1}{8} cos (8 x) + C

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What is the integral of tan(8x)sin(8x)cot(8x) ?
The integral of tan(8x)sin(8x)cot(8x) is -1/8 cos(8x)+C