## PART - 1

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This part is based on following particular functions:
$\int \frac{1}{x^2-a^2} dx = \frac{1}{2a} \log \left | \frac{x-a}{x+a} \right | + C$

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

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

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

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

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## PART - 2

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Questions discussed in this lecture:
1. $\int \frac{3x^2}{x^6+1} dx$

2. $\int \frac{1}{\sqrt{1+4x^2}} dx$

3. $\int \frac{1}{\sqrt{(2-x)^2+1}} dx$

4. $\int \frac{1}{\sqrt{9-25x^2}} dx$

5. $\int \frac{3x}{1+2x^4} dx$

6. $\int \frac{x^2}{1-x^6} dx$

7. $\int \frac{x-1}{\sqrt{x^2-1}} dx$

8. $\int \frac{x^2}{\sqrt{x^6+a^6}} dx$

9. $\int \frac{\sec^2 x}{\sqrt{\tan^2 x+4}} dx$