# NCERT Exercise 7.4

## 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