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

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

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integral of sec^2(x)-5

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

tan (x) - 5 x + C

Solution steps

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

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

\int 5 d x = 5 x

= tan (x) - 5 x

Add a constant to the solution

= tan (x) - 5 x + C

\frac{d y}{d t} = 2 \cdot y

x^{2} - 5

x \to \infty lim (- 3 e^{x})

\frac{d}{d x} (- \frac{y}{y ^{2} + x ^{2}})

\frac{d}{d x} (cos^{4} (x) - 2 x^{2})