## Part - 9 Lecture - 4 Chapter 7 Integrals

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“Failure Will Never Overtake Me If My Determination To Succeed Is Strong Enough.” – Og Mandino

**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.

9. \int \frac{3x^2dx}{x^6+1}={\tan}^{-1}{x^3}+C

10. \int \frac{x^2}{1-x^6}dx=\frac{1}{6} \log {\left|\frac{1+x^3}{1-x^3}\right|}+C

11. \int \frac{x^2}{\sqrt{x^6+a^6}} dx = \frac{1}{3} \log \left | x^3 + \sqrt{x^6+a^6} \right | +C

12. \int \frac{x^3}{\sqrt{1-x^8}}dx=\frac{1}{4}{\sin}^{-1}{(}x^4)+C

13. \int \frac{x+2}{\sqrt{x^2-1}}dx=\sqrt{x^2-1}+2 \log {\left|x+\sqrt{x^2-1}\right|}+C

14. \int \sqrt{1-\frac{x^2}{9}}dx=\frac{1}{3}\left[\frac{x}{2}\sqrt{9-x^2}+\frac{9}{2}{\sin}^{-1}{\frac{x}{3}}\right]+C