Dr.Harswaroop Sharma Mathematics Solution Class 12 Chapter 7 समाकलन (Integration) Exercise 7N

    

प्रश्नावली - 7N

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Question 1

निम्न समाकलों के मान ज्ञात कीजिए
1. (a) $\int \frac{d x}{x^2-9}$
(b) $\int \frac{d x}{24-6 x^2}$

(c) $\int \frac{d x}{x^2-7}$

(d) $\int \frac{d x}{(x+3)^2-4}$

(e) $\int \frac{2 x}{x^2+3 x+2} d x$

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Question 2

2. (a) $\int \frac{2 x}{x^2+3 x+2} d x$
(b) $\int \frac{(2 x+1) d x}{(x+1)(x-2)}$

(c) $\int \frac{5 x d x}{(x+1)\left(x^2-4\right)}$

(d) $\int \frac{3 x d x}{(x-2)(x+1)}$

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Question 3

3. (a) $\int \frac{\cos x d x}{(1-\sin x)(2-\sin x)}$
(b) $\int \frac{\sec ^2 x d x}{(\tan x+1)(\tan x+2)}$

(c) $\int \frac{(2 x-3) d x}{\left(x^2-1\right)(2 x+3)}$

(d) $\int \frac{d x}{\left(x^2+1\right)\left(x^2+4\right)}$

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Question 4

4. (a) $\int \frac{x^3+3}{x^3-3 x} d x$
(b) $\int \frac{x^3+x+1}{x^2-1} d x$

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Question 5

5. (a) $\int \frac{x^2}{x^6+x^3-2} d x$
(b) $\int \frac{e^x d x}{\left(1+e^x\right)\left(2+e^x\right)}$

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Question 6

6. (a) $\int \frac{d x}{x(x+1)^2}$
(b) $\int \frac{x d x}{(x-1)^2(x+2)}$

(c) $\int \frac{x d x}{x^2+2 x+1}$

(d) $\int \frac{(x+1) d x}{(x+1)^2(x-2)}$

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Question 7

7. $\int \frac{x d x}{\left(x^2+1\right)(x-1)}$

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Question 8

8. $\int \frac{x d x}{(x-1)(x-2)(x-3)}$

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Question 9

9. (a) $\int \frac{\left(x^2+1\right)\left(x^2+2\right)}{\left(x^2+3\right)\left(x^2+4\right)} d x$
(b) $\int \frac{(x+1) d x}{(x-1)\left(x^2+1\right)^2}$

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Question 10

10. (a) $\int \frac{d x}{x^4-a^4}$
(b) $\int \frac{d x}{\left(x^2+a^2\right)\left(x^2+b^2\right)}$

(c) $\int \frac{2 x}{\left(x^2+1\right)\left(x^2+3\right)} d x$

(d) $\int \frac{x^2 d x}{\left(x^2+1\right)\left(x^2+4\right)}$

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Question 11

11. $\int \frac{d x}{x\left(x^n+1\right)}$

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Question 12

12. $\int \frac{d x}{x^4-1}$

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Question 13

13. $\int \frac{d x}{1-\sin ^4 x}$

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Question 14

14. $\int \frac{\left(x^2+x+1\right)}{(x+1)^2(x+2)} d x$

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Question 15

15. $\int \frac{2 d x}{(1-x)\left(1+x^2\right)} d x$

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Question 16

16. $\int \frac{\sin x}{\sin ^3 x+\cos ^3 x} d x$

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Question 17

17. $\int \frac{(3 x+5)}{x^3-x^2-x+1} d x$

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Question 18

18. $\int \frac{e^x-2}{e^{2 x}+4} d x$

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Question 19

19. $\int \frac{(3 x-1)}{(x-1)(x-2)(x-3)} d x$