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

Question 1

निम्नलिखित फलनों का $x$ के सापेक्ष समाकल ज्ञात कीजिये :
1. $\sec x \tan x \sqrt{\sec ^2 x+1}$.

Question 2

2. $\frac{1}{\log x}-\frac{1}{(\log x)^2}$.

Question 3

3. $e^x\left(\frac{1}{x}-\frac{1}{x^2}\right)$

Question 4

4. $e^x(1+\tan x) \sec x$.

Question 5

5. $\frac{x \sin x}{\cos ^2 x}$.

Question 6

6. $e^x(\sin x+\cos x)$.

Question 7

7. $x \cot ^2 x$.

Question 8

8. $\left(x^2 \sqrt{x^6-1}\right)$.

Question 9

9. $\frac{\log \sec ^{-1} x}{x \sqrt{x^2-1}}$

Question 10

10. $x^2 \sin x \cos x$.

Question 11

11. $\frac{x-\sin x}{1-\cos x}$.

Question 12

12. $\frac{e^x(1-\sin x)}{1-\cos x}$.

Question 13

13. $e^x \sin x \cos x \cos 2 x$.

Question 14

14. $e^x\left(\frac{2+\sin 2 x}{1+\cos 2 x}\right)$

Question 15

15. $\frac{x e^x}{(x+1)^2}$.

Question 16

16. $\frac{\log _e x}{(1+\log x)^2}$.

Question 17

17. $e^x\left(\frac{x+2}{x+4}\right)^2$

Question 18

18. $\frac{5 \sin \left(\log _e x\right)}{x^3}$

Question 19

19. सिद्ध कीजिए कि $\int e^{\tan ^{-1} x} \cdot\left(\frac{1+x+x^2}{1+x^2}\right) d x=x e^{\tan ^{-1} x}+c$.

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