What is the integral of (3csc^2(x)-5sec(x)tan(x)) ?

The integral of (3csc^2(x)-5sec(x)tan(x)) is -3cot(x)-5sec(x)+C

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integral of (3csc^2(x)-5sec(x)tan(x))

\int (3 csc^{2} (x) - 5 sec (x) tan (x)) d x

- 3 cot (x) - 5 sec (x) + C

Solution steps

\int 3 csc^{2} (x) - 5 sec (x) tan (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 3 csc^{2} (x) d x - \int 5 sec (x) tan (x) d x

\int 3 csc^{2} (x) d x = - 3 cot (x)

\int 5 sec (x) tan (x) d x = 5 sec (x)

= - 3 cot (x) - 5 sec (x)

Add a constant to the solution

= - 3 cot (x) - 5 sec (x) + C

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What is the integral of (3csc^2(x)-5sec(x)tan(x)) ?
The integral of (3csc^2(x)-5sec(x)tan(x)) is -3cot(x)-5sec(x)+C