What is the integral of (sec^2(x)-8) ?

The integral of (sec^2(x)-8) is tan(x)-8x+C

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integral of (sec^2(x)-8)

\int (sec^{2} (x) - 8) d x

tan (x) - 8 x + C

Solution steps

\int sec^{2} (x) - 8 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 sec^{2} (x) d x - \int 8 d x

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

\int 8 d x = 8 x

= tan (x) - 8 x

Add a constant to the solution

= tan (x) - 8 x + C

\int cos (2 x) sin (2 x) d x

\frac{1}{2} + \frac{1}{2} \cdot cos (2 t)

\int \frac{2000}{300 x} d x

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

\frac{d}{d x} (1 + 3 x)

What is the integral of (sec^2(x)-8) ?
The integral of (sec^2(x)-8) is tan(x)-8x+C