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

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

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

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

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

Solution steps

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

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} (t) d t - \int 5 sec (t) tan (t) d t

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

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

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

Add a constant to the solution

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

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