What is the integral of (4csc(x)cot(x)+2sec^2(x)) ?

The integral of (4csc(x)cot(x)+2sec^2(x)) is -4csc(x)+2tan(x)+C

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integral of (4csc(x)cot(x)+2sec^2(x))

\int (4 csc (x) cot (x) + 2 sec^{2} (x)) d x

- 4 csc (x) + 2 tan (x) + C

Solution steps

\int 4 csc (x) cot (x) + 2 sec^{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 4 csc (x) cot (x) d x + \int 2 sec^{2} (x) d x

\int 4 csc (x) cot (x) d x = - 4 csc (x)

\int 2 sec^{2} (x) d x = 2 tan (x)

= - 4 csc (x) + 2 tan (x)

Add a constant to the solution

= - 4 csc (x) + 2 tan (x) + C

What is the integral of (4csc(x)cot(x)+2sec^2(x)) ?
The integral of (4csc(x)cot(x)+2sec^2(x)) is -4csc(x)+2tan(x)+C