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

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

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integral of-sec^2(x)

integral

- sec^{2} (x)

- tan (x) + C

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Use the common integral:

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

= - tan (x)

Add a constant to the solution

= - tan (x) + C