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Integrals of simple functions

List of integrals of rational functions









Any rational function can be integrated using above equations and partial fractions in integration, by decomposing the rational function into a sum of functions of the form:


Irrational functions

Absolute Value Functions


Exponential functions

Trigonometric functions

Hyperbolic functions


Inverse hyperbolic functions

Definite integrals lacking closed-form antiderivatives

   (if n is an even integer and )

>(if  \scriptstyle{n} is an odd integer and )

(where Γ(z) is the Gamma function)

(where exp[u] is the exponential function eu, and a > 0)

(where I0(x) is the modified Bessel function of the first kind)

, \nu > 0\,, this is related to the probability density function of the Student's t-distribution)

The method of exhaustion provides a formula for the general case when no antiderivative exists:

The "sophomore's dream"

"Chance favors the prepared mind." - Louis Pasteur