What is the antiderivative of tanx?

The antiderivative of tan(x) is given by -ln|cos(x)| + C, where C is the constant of integration. This formula can be derived using integration by parts or by using trigonometric identities.

It is important to note that the antiderivative of tan(x) is not always well-defined, as tan(x) is not defined at certain values of x where cos(x) = 0. In these cases, the antiderivative may be expressed using a different form or as an improper integral.

The antiderivative of tan(x) can also be written as -ln|cos(x)| + ln|sec(x)| + C, as the two expressions are equivalent due to the trigonometric identity tan(x) = sin(x)/cos(x) and the relationship between sec(x) and cos(x).

When working with the antiderivative of tan(x), it is important to be mindful of the domain of the function and any restrictions that may apply.