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Integrals of simple functions

List of integrals of rational functions

for

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:

.

>

(if *n* is an even integer and )

>(if is an odd integer and )

(where
Γ(*z*) is the Gamma function)

(where exp[*u*]
is the exponential function *e ^{u}*,
and

(where
*I*_{0}(*x*) is the modified
Bessel function of the first kind)

, , 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:

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