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

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

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

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

tan (x) - 2 x + C

Solution steps

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

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

\int 2 d x = 2 x

= tan (x) - 2 x

Add a constant to the solution

= tan (x) - 2 x + C

\int_{0}^{2} \frac{2}{2 - x} d x

\int_{0}^{1} e^{- 8 x} d x

x \to \infty lim \frac{( e ^{\frac{15}{x}} - 1 )}{\frac{15}{x}}

(s + \frac{3}{2})^{2}

\int e^{\frac{- x}{k}} \cdot \frac{- x}{k} d x

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