Q:

# What is the antiderivative of tan?

A:

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.

## Keep Learning

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.

Sources:

## Related Questions

• A: The derivative of secant is equal to the tangent of x times the secant of x. Expressed in mathematical terms, the equation reads as d/dx secant(x) = tan(x)... Full Answer >
Filed Under:
• A: The integral of cosine squared is equal to x/2 + (1/4)sin(2x) + C, where C is a constant. The integral can be solved by using the half-angle identity of th... Full Answer >
Filed Under:
• A: The cosine of 1 is 0.99 when evaluated in degrees and 0.54 when evaluated in radians. The value can be found by using the cosine function on a calculator o... Full Answer >
Filed Under:
• A: The abbreviations "sin," "cos," "tan," "csc," "sec" and "cot" stand for the six trigonometric functions: sine, cosine, tangent, cosecant, secant and cotang... Full Answer >
Filed Under:
PEOPLE SEARCH FOR