प्रश्नावली - 7T
निम्न समाकलों का मान ज्ञात कीजिए:
1. $\int \frac{d x}{x^4-1}$
2. $\int \frac{(1+x)}{x(x-1)^2} d x$
3. $\int \frac{d x}{2 x^2+5 x+3}$
4. $\int \frac{d x}{\sqrt{4+3 x-2 x^2}}$
5. $\int \frac{2 x+1}{\sqrt{4 x^2+5 x+6}} d x$
6. $\int \frac{x+2}{\sqrt{x^2-1}} d x$
7. $\int \frac{d x}{\left(x^2+1\right)^3}$
8. $\int \frac{d x}{x\left(x^2+1\right)^3}$
9. $\int \frac{d x}{4 \sin ^2 x+9 \cos ^2 x}$
10. $\int \frac{d x}{a^2-b^2 \cos ^2 x}, a>b$
11. $\int \frac{d \theta}{\sin ^4 \theta+\cos ^4 \theta}$
12. $\int \frac{d x}{\sqrt{x^2+3 x+1}}$
13. $\int \frac{x d x}{\sqrt{9+8 x-x^2}}$
14. $\int \frac{d x}{(2 \sin x+3 \cos x)^2}$
15. $\int \frac{\sin x d x}{\sin x-\cos x}$
16. $\int \frac{x-1}{\sqrt{x^2-1}} d x$
17. $\int \frac{\sec ^2 x}{\sqrt{\tan ^2 x+4}} d x$
18. $\int \frac{d x}{\sqrt{x^2+2 x+2}}$
19. $\int \frac{d x}{\sqrt{7-6 x-x^2}}$
20. $\int \frac{d x}{\sqrt{(x-1)(x-2)}}$
21. $\int \frac{d x}{\sqrt{8+3 x-x^2}}$
22. $\int \frac{d x}{\sqrt{(x-a)(x-b)}}$
23. $\int \frac{(4 x+1)}{\sqrt{2 x^2+x-3}} d x$
24. $\int \frac{(6 x+7)}{\sqrt{(x-5)(x-4)}} d x$
25. $\int \frac{x+2}{\sqrt{4 x-x^2}} d x$
26. $\int \frac{x+2}{\sqrt{x^2+2 x+3}} d x$
27. $\int \frac{5 x+3}{\sqrt{x^2+4 x+10}} d x$
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