The antiderivative of the tangent of x equals the negative natural log of the absolute value of the cosine of x, plus a constant. In mathematical terms, the antiderivative can be expressed as = - ln |cos(x)| + C.
The antiderivative is also known as the integral. The integral of the tangent of x can be written as the integral of sine over cosine. Since negative sine is the derivative of cosine, the formula can be rewritten as the negative sine of x over the cosine of x. When solving the integral, the equation must take the natural log of the absolute value because it is impossible to take the natural log of a negative number.