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 20, 2023

Jun 26, 2023

Jun 23, 2023

Latest Math Problems

Jul 01, 2023

Jun 25, 2023

Copyright © 2012 - 2023 Math Doubts, All Rights Reserved