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

\int (x + 1) x + 3 d x

\frac{d y}{d x} = 4 x^{3} y

\frac{\partial}{\partial x} (- 2 y sin (x))

y^{^{''}} + 4 y = e^{- t}

7 (4 e^{x} - 27)^{5}

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