PART – 1

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

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

PART – 3

Questions discussed in this lecture:
10. $$int frac{1}{sqrt{x^2+2x+2}} dx$$

11. $$int frac{1}{9x^2+6x+5} dx$$

12. $$int frac{1}{sqrt{7-6x-x^2}} dx$$

13. $$int frac{1}{sqrt{(x-1)(x-2)}} dx$$

14. $$int frac{1}{sqrt{8+3x-x^2}} dx$$

15. $$int frac{1}{sqrt{(x-a)(x-b)}} dx$$

PART – 4

Questions discussed in this lecture:
17. $$int frac{x+2}{sqrt{x^2-1}} dx$$

18. $$int frac{5x-2}{1+2x+3x^2} dx$$

PART – 5

Questions discussed in this lecture:
19. $$int frac{6x+7}{sqrt{(x-5)(x-4)}} dx$$

20. $$int frac{x+2}{sqrt{4x-x^2}} dx$$