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Integrals of simple 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:

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Irrational functions

Absolute Value Functions

Logarithms

Exponential functions

Trigonometric functions

Hyperbolic functions

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Inverse hyperbolic functions

Definite integrals lacking closed-form antiderivatives

   (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 a > 0)

(where I₀(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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