What is the integral of (cos(8x)-csc^2(x)) ?

The integral of (cos(8x)-csc^2(x)) is 1/8 sin(8x)+cot(x)+C

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integral of (cos(8x)-csc^2(x))

\int (cos (8 x) - csc^{2} (x)) d x

\frac{1}{8} sin (8 x) + cot (x) + C

Solution steps

\int cos (8 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 (8 x) d x - \int csc^{2} (x) d x

\int cos (8 x) d x = \frac{1}{8} sin (8 x)

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

= \frac{1}{8} sin (8 x) - (- cot (x))

Simplify

= \frac{1}{8} sin (8 x) + cot (x)

Add a constant to the solution

= \frac{1}{8} sin (8 x) + cot (x) + C

\frac{d}{d x} (x e^{s i n (x)})

n = 1 \sum \infty \frac{3 ^{n + 2}}{5 ^{n}}

(r^{5} - 4 r) e^{r}

\frac{d y}{d x} = (y^{2} - 9), y (1) = 4

\int e^{x} cos (\frac{x}{2}) d x

What is the integral of (cos(8x)-csc^2(x)) ?
The integral of (cos(8x)-csc^2(x)) is 1/8 sin(8x)+cot(x)+C