Lecture 4 Integrals Class 12 Maths Part 9

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Part - 9 Lecture - 4 Chapter 7 Integrals

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

Booklets/Notes/Assignments are typed here on this website and their PDFs will be made available soon.

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

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