Math Doubts

Integral rules of irrational functions

The irrational functions are come in integral calculus and it is not possible to find the integration of the irrational functions with the standard integral rules. Hence, it requires some special integral formulas in some cases to evaluate the integrals of the irrational functions. The following are the integral rules of the irrational functions with proofs.

Sum of squares

$\displaystyle \int{\dfrac{1}{\sqrt{x^2+a^2}}}\,dx$ $\,=\,$ $\log_{e}{\Big|x+\sqrt{x^2+a^2}\Big|}+c$

Difference of squares

$\displaystyle \int{\dfrac{1}{\sqrt{x^2-a^2}}}\,dx$ $\,=\,$ $\log_{e}{\Big|x+\sqrt{x^2-a^2}\Big|}+c$

$\displaystyle \int{\dfrac{1}{\sqrt{a^2-x^2}}}\,dx$ $\,=\,$ $\arcsin{\bigg(\dfrac{x}{a}\bigg)}+c$ or $\sin^{-1}{\bigg(\dfrac{x}{a}\bigg)}+c$

Math Doubts

A best free mathematics education website that helps students, teachers and researchers.

Maths Topics

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

Maths Problems

A math help place with list of solved problems with answers and worksheets on every concept for your practice.

Learn solutions

Subscribe us

You can get the latest updates from us by following to our official page of Math Doubts in one of your favourite social media sites.

Copyright © 2012 - 2022 Math Doubts, All Rights Reserved