What is the integral of csc^2(8θ)cot(8θ) ?

The integral of csc^2(8θ)cot(8θ) is -1/16 cot^2(8θ)+C

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integral of csc^2(8θ)cot(8θ)

\int csc^{2} (8 θ) cot (8 θ) d θ

- \frac{1}{16} cot^{2} (8 θ) + C

Solution steps

\int csc^{2} (8 θ) cot (8 θ) d θ

Apply u-substitution

: \int - \frac{u}{8} d u

= \int - \frac{u}{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 u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

= - \frac{1}{8} \cdot \frac{u ^{2}}{2}

Substitute back

u = cot (8 θ)

= - \frac{1}{8} \cdot \frac{cot ^{2} ( 8 θ )}{2}

Simplify

- \frac{1}{8} \cdot \frac{cot ^{2} ( 8 θ )}{2} : - \frac{1}{16} cot^{2} (8 θ)

= - \frac{1}{16} cot^{2} (8 θ)

Add a constant to the solution

= - \frac{1}{16} cot^{2} (8 θ) + C

f (θ) = cos (θ^{2})

\int_{0}^{1} x^{2} sin (nπ x) d x

\int tan^{2} (3 x - 1) d x

\int 5 x^{- \frac{6}{7}} d x

x \to 3 lim (\frac{x - 2}{6 - 2 x})

What is the integral of csc^2(8θ)cot(8θ) ?
The integral of csc^2(8θ)cot(8θ) is -1/16 cot^2(8θ)+C