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

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

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

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

2 sec (x) - 5 tan (x) + C

Solution steps

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

\int 2 sec (x) tan (x) d x = 2 sec (x)

\int 5 sec^{2} (x) d x = 5 tan (x)

= 2 sec (x) - 5 tan (x)

Add a constant to the solution

= 2 sec (x) - 5 tan (x) + C

\frac{d}{d x} ((x^{3} + 5 x)^{2} (5 x - 3)^{4})

f (x) = tan (7 x)

\int \frac{1}{x ( x ^{3} + 1 ) ^{2}} d x

e^{7 t s i n (2 t)}

f (x) = \frac{- 2 x}{x ^{2} + 1}, at x = 1

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