# Lecture 4 Part 2 Integrals Class 12 Maths

INTEGRATION OF ALGEBRAIC FUNCTIONS

SECOND METHOD

In the second method, we use integrals of some particular functions to find the integrals of our rational functions.

Play Video

Derivation of PARTICULAR CASES

$\int \frac{dx}{x^2-a^2}=\frac{1}{2a}\log{\left|\frac{x-a}{x+a}\right|}+C$

$\int \frac{dx}{\sqrt{x^2\pm a^2}}= \log{\left|x+\sqrt{x^2\pm a^2}\right|}+C$

$\int\frac{dx}{x^2+a^2}=\frac{1}{a}{\tan}^{-1}{\frac{x}{a}}+C$

$\int \frac{dx}{a^2-x^2}=\frac{1}{2a}\log{\left|\frac{a+x}{a-x}\right|}+C$

$\int \frac{dx}{\sqrt{a^2-x^2}}={\sin}^{-1}{\frac{x}{a}}+C$

$\int \sqrt{x^2\pm a^2}=\frac{x}{2}\sqrt{x^2\pm a^2}\pm\frac{a^2}{2}\log\left|x+\sqrt{x^2\pm a^2}\right|+C$

$\int \sqrt{a^2-x^2}=\frac{x}{2}\sqrt{a^2-x^2}+\frac{a^2}{2}{\sin}^{-1}{\frac{x}{a}}+C$