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

    

प्रश्नावली - 7J

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Question 1

निम्नलिखित समाकल का मान ज्ञात कीजिए-
1. (a) $\int x^2 \log _e x d x$
(b) $\int \log _e\left(1+x^2\right) d x$
(c) $\int x \log _e x d x$
(d) $\int\left(\log _e x\right)^2 d x$

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Question 2

2. (a) $\int x \cos x d x$
(b) $\int \sec ^3 x d x$

(c) $\int x^2 \sin 2 x d x$

(d) $\int x \operatorname{cosec}^2 a x d x$

(e) $\int x \sec ^2 x d x$

(f) $\int x \sec ^2 2 x d x$

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Question 3

3. (a) $\int \sin ^{-1} x d x$
(b) $\int \cot ^{-1} x d x$

(c) $\int x \sin ^{-1} x d x$

(d) $\int x \cos ^{-1} x d x$

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Question 4

4. (a) $\int x \log _e 2 x d x$
(b) $\int \log _{10} x d x$

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Question 5

5. (a) $\int x e^{a x} d x$
(b) $\int \frac{e^{1 / x}}{x^3} d x$

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Question 6

6. (a) $\int x \sin 3 x d x$
(b) $\int x \sin ^2 x d x$

(c) $\int x \tan ^2 x d x$

(d) $\int \frac{(x-3) e^x}{(x-1)^3} d x$

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Question 7

7. (a) $\int x^3 \tan ^{-1} x d x$
(b) $\int \frac{\log _e x}{(1+x)^2} d x$
(c) $\int\left(\sin ^{-1} x\right)^2 d x$

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Question 8

8. $\int \frac{x^2}{(x \sin x+\cos x)^2} d x$

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Question 9

9. $\int x\left(\log _e x\right)^2 d x$

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Question 10

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

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Question 11

11. $\int x^2 e^x d x$

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Question 12

12. $\int \sin x \log _e(\sec x+\tan x) d x$

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Question 13

13. $\int \sec x \log (\sec x+\tan x) d x$

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Question 14

14. $\int\left(x^2+1\right) \log x d x$

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Question 15

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