What is the integral of 5cos(x)-csc^2(x) ?

The integral of 5cos(x)-csc^2(x) is 5sin(x)+cot(x)+C

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integral of 5cos(x)-csc^2(x)

\int 5 cos (x) - csc^{2} (x) d x

5 sin (x) + cot (x) + C

Solution steps

\int 5 cos (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 5 cos (x) d x - \int csc^{2} (x) d x

\int 5 cos (x) d x = 5 sin (x)

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

= 5 sin (x) - (- cot (x))

Simplify

= 5 sin (x) + cot (x)

Add a constant to the solution

= 5 sin (x) + cot (x) + C

What is the integral of 5cos(x)-csc^2(x) ?
The integral of 5cos(x)-csc^2(x) is 5sin(x)+cot(x)+C