Q:

What is the antiderivative of sec(x)?

A:

Quick Answer

The antiderivative of sec(x) is equal to ln |sec(x) + tan(x)| + C, where C represents a constant. This antiderivative, also known as an integral, can be solved by using the integration technique known as substitution.

Continue Reading

Full Answer

The antiderivative of sec(x) is equal to the antiderivative of sec(x) * ([sec(x) + tan(x])/[sec(x) + tan(x)]). Using substitution, the variable u replaces sec(x) + tan(x), and the derivative of u, du, is (sec(x) * tan(x) + sec^2(x)) dx. Substituting u and du into the equation for the integral of ([sec^2(x) + sec(x) * tan (x) dx]/[sec(x) + tan(x)]) results in the integral of du/u. Solving that integral gives ln |u| + C, and substituting back in for u gives the above solution.

Learn more about Calculus

Related Questions

Explore