What is the integral of 4sec(x)tan(x)-2sec^2(x) ?

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

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integral of 4sec(x)tan(x)-2sec^2(x)

integral

4 sec (x) tan (x) - 2 sec^{2} (x)

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

Solution steps

\int 4 sec (x) tan (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 sec (x) tan (x) d x - \int 2 sec^{2} (x) d x

\int 4 sec (x) tan (x) d x = 4 sec (x)

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

= 4 sec (x) - 2 tan (x)

Add a constant to the solution

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

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