What is the integral of 9/(1-cos^2(x)) ?

The integral of 9/(1-cos^2(x)) is -9cot(x)+C

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integral of 9/(1-cos^2(x))

\int \frac{9}{1 - cos ^{2} ( x )} d x

- 9 cot (x) + C

Solution steps

\int \frac{9}{1 - cos ^{2} ( x )} d x

Take the constant out:

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

= 9 \cdot \int \frac{1}{1 - cos ^{2} ( x )} d x

Rewrite using trig identities

= 9 \cdot \int csc^{2} (x) d x

Use the common integral:

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

= 9 (- cot (x))

Simplify

= - 9 cot (x)

Add a constant to the solution

= - 9 cot (x) + C

\frac{d}{d x} (3 x^{2} - 18 x + 15)

\frac{4 s}{s ^{2} + 9}

\frac{d}{d y} ((\frac{1}{y ^{2}} - \frac{9}{y ^{4}}) (y + 7 y^{3}))

\frac{\partial}{\partial x} (ln (x e^{- 6 x}))

x \to + 0 lim ((\frac{1}{x ^{2}})^{2})

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