What is the integral of (csc^2(θ)+9) ?

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

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integral of (csc^2(θ)+9)

\int (csc^{2} (θ) + 9) d θ

- cot (θ) + 9 θ + C

Solution steps

\int csc^{2} (θ) + 9 d θ

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int csc^{2} (θ) d θ + \int 9 d θ

\int csc^{2} (θ) d θ = - cot (θ)

\int 9 d θ = 9 θ

= - cot (θ) + 9 θ

Add a constant to the solution

= - cot (θ) + 9 θ + C

f (x) = cos (x), 0, \frac{π}{4}

f (x) = \frac{x ^{3}}{2} - \frac{4}{3 x}, at x = 2

y = e^{m x} m

\frac{d}{d x} (3 x^{2} - 3 x)

(y^{3} - x y^{2}) d x + 2 x^{2} y d y = 0

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