## Part - 7 Lecture - 4 Chapter 7 Integrals

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**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.

**Derivation of PARTICULAR CASES**

\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

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