What is the integral of csc^2(9θ+2) ?

The integral of csc^2(9θ+2) is -1/9 cot(9θ+2)+C

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integral of csc^2(9θ+2)

\int csc^{2} (9 θ + 2) d θ

- \frac{1}{9} cot (9 θ + 2) + C

Solution steps

\int csc^{2} (9 θ + 2) d θ

Apply u-substitution

: \int csc^{2} (u) \frac{1}{9} d u

= \int csc^{2} (u) \frac{1}{9} d u

Take the constant out:

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

= \frac{1}{9} \cdot \int csc^{2} (u) d u

Use the common integral:

\int csc^{2} (u) d u = - cot (u)

= \frac{1}{9} (- cot (u))

Substitute back

u = 9 θ + 2

= \frac{1}{9} (- cot (9 θ + 2))

Simplify

= - \frac{1}{9} cot (9 θ + 2)

Add a constant to the solution

= - \frac{1}{9} cot (9 θ + 2) + C

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What is the integral of csc^2(9θ+2) ?
The integral of csc^2(9θ+2) is -1/9 cot(9θ+2)+C