Mathematics Magazine
Home Online Math Tests Math Book Subscribe Contact Us
Bookmark and Share Advertise Here. E-mail us your request for an advertising quote!

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:

.

Irrational functions

Absolute Value Functions

Logarithms

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