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.

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

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

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

Latest Math Topics

Jul 24, 2022

Jul 15, 2022

Latest Math Problems

Jul 29, 2022

Jul 17, 2022

Jun 02, 2022

Apr 06, 2022

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

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

Learn how to solve the maths problems in different methods with understandable steps.

Copyright © 2012 - 2022 Math Doubts, All Rights Reserved