What Are Some Common Antiderivatives of Trig Functions?

What Are Some Common Antiderivatives of Trig Functions?

The antiderivative of the cosine function is sin x + c, and the antiderivative of the sine function is -cos x + c. The antiderivative of the tangent function is equal to ln |sec x| + c. The antiderivative is also known as the integral.

Other common trigonometric functions with antiderivatives include secant, cosecant and cotangent. The integral of cosecant is equal to ln |csc x - cot x| + c, while the integral of the secant function is ln |sec x + tan x| + c.

The mathematical notation ln represents the natural logarithm, which is also equivalent to the logarithm to the base of e. The straight lines in the function indicate the absolute value, as natural logarithm function requires a positive number.

The antiderivative for the cotangent is ln |sin x| + c. The inverses of trigonometric functions also have antiderivatives. For example, the integral of the inverse sine function is u times the inverse sine of u, plus the square root of 1 minus u squared, plus c.

The integral of the inverse tangent function is equal to u times the inverse tangent of u, minus one-half of the natural logarithm of 1 plus u squared plus c. Integration techniques for trig functions include substitution and partial fraction methods.