What is the integral of sec^2(x)-6 ?

The integral of sec^2(x)-6 is tan(x)-6x+C

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integral of sec^2(x)-6

\int sec^{2} (x) - 6 d x

tan (x) - 6 x + C

Solution steps

\int sec^{2} (x) - 6 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 6 d x

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

\int 6 d x = 6 x

= tan (x) - 6 x

Add a constant to the solution

= tan (x) - 6 x + C

\frac{\partial}{\partial y} (3 x^{2} y^{4} + 1)

\frac{\partial}{\partial x} (4 x^{3} y^{2} - 4 x^{2} + y^{6} + 1)

\int_{0}^{1} x cos (x) d x

\int_{2}^{6} x^{2} d x

\frac{\partial}{\partial y} (3 x^{2} - 3 y^{2})