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

निम्नलिखित समाकल का मान ज्ञात कीजिए-

Question 1

1. $\int \frac{x \cos ^{-1} x}{\sqrt{1-x^2}} d x$

Question 2

2. $\int \sin ^{-1} \sqrt{\frac{x}{a+x}} d x$.

Question 3

3. $\int \frac{\sin ^{-1} x}{\left(1-x^2\right)^{3 / 2}} d x$.

Question 4

4. $\int \tan ^{-1}\left(\frac{3 x-x^3}{1-3 x^2}\right) d x$.

Question 5

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

Question 6

6. $\int \cos x \sqrt{4-\sin ^2 x} d x$.

Question 7

7. $\int \frac{\sin \left(\log _e x\right)}{x^3} d x$.

Question 8

8. $\int \frac{m \tan ^{-1} x}{\left(1+x^2\right)^{3 / 2}} d x$.

Question 9

9. $\int \tan ^{-1} \sqrt{\frac{1-x}{1+x}} d x$.

Question 10

10. $\int \operatorname{cosec}^{-1} \sqrt{\frac{x+a}{x}} d x$.

Question 11

11. $\int x \sin ^{-1} \frac{1}{2} \sqrt{\left(\frac{2 a-x}{a}\right)} d x$.

Question 12

12. $\int \cos \left[2 \cot ^{-1} \sqrt{\frac{1-x}{1+x}}\right] d x$.

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