What is the integral of (cos(6x)-csc^2(x)) ?

The integral of (cos(6x)-csc^2(x)) is 1/6 sin(6x)+cot(x)+C

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integral of (cos(6x)-csc^2(x))

\int (cos (6 x) - csc^{2} (x)) d x

\frac{1}{6} sin (6 x) + cot (x) + C

Solution steps

\int cos (6 x) - csc^{2} (x) d x

Apply the Sum Rule:

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

= \int cos (6 x) d x - \int csc^{2} (x) d x

\int cos (6 x) d x = \frac{1}{6} sin (6 x)

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

= \frac{1}{6} sin (6 x) - (- cot (x))

Simplify

= \frac{1}{6} sin (6 x) + cot (x)

Add a constant to the solution

= \frac{1}{6} sin (6 x) + cot (x) + C

What is the integral of (cos(6x)-csc^2(x)) ?
The integral of (cos(6x)-csc^2(x)) is 1/6 sin(6x)+cot(x)+C