प्रश्नावली - 7E
Question 1
निम्नलिखित के मान ज्ञात कीजिए
1. (a) $\int \sin ^4 x \cos x d x$
(b) $\int \cos ^2 x \sin x d x$
(c) $\int \cot ^2 x \operatorname{cosec}^2 x d x$
(d) $\int \sec ^p x \tan x d x$
(e) $\int \sin x \cos x d x$Question 2
2. (a) $\int \frac{\left(\log _e x\right)^3}{x} d x$
(b) $\int \frac{\sin \left(\log _e x\right)}{x} d x$
(c) $\int \frac{1+\log _e x}{x} d x$
(d) $\int \frac{1}{x \cos ^2\left(\log _e x\right)} d x$
Question 3
निम्नलिखित के मान ज्ञात कीजिए
3. (a) $\int e^x \sin e^x d x$
(b) $\int e^x\left(4+5 e^x\right)^n d x$
(c) $\int \frac{e^{m \sin ^{-1} x}}{\sqrt{1-x^2}} d x$
(d) $\int e^{\tan x} \sec ^2 x d x$
Question 4
निम्नलिखित के मान ज्ञात कीजिए
4. (a) $\int \frac{\tan ^{-1} x}{\left(1+x^2\right)^{3 / 2}} d x$
(b) $\int \frac{\tan ^{-1} x}{1+x^2} d x$
Question 5
5. $\int \frac{1}{\sqrt{x}[\sqrt{x}+1]} d x$
Question 6
6. $\int \frac{\log _e x \sin \left[1+\left(\log _e x\right)^2\right]}{x} d x$
Question 7
7. $x \sqrt{1+2 x^2}$
Question 8
8. $\int \frac{d x}{\cos ^2 x(1-\tan x)^2}$
Question 9
9. $\int \frac{x \tan ^{-1} x^2}{1+x^4} d x$
Question 10
10. (a) $\int \frac{x^3 \sin \left(\tan ^{-1} x^4\right)}{1+x^8} d x$
(b) $\int \frac{1}{x^2 \cos ^2\left(\frac{1}{x}\right)} d x$
(b) $\int \frac{\tan ^{-1} x}{1+x^2} d x$
(c) $\int \frac{\left(\sin ^{-1} x\right)}{\sqrt{1-x^2}} d x$
(d) $\int \frac{\sec ^{-1} x}{x \sqrt{x^2-1}} d x$
Question 5
5. $\int \frac{1}{\sqrt{x}[\sqrt{x}+1]} d x$
Question 6
6. $\int \frac{\log _e x \sin \left[1+\left(\log _e x\right)^2\right]}{x} d x$
Question 7
7. $x \sqrt{1+2 x^2}$
Question 8
8. $\int \frac{d x}{\cos ^2 x(1-\tan x)^2}$
Question 9
9. $\int \frac{x \tan ^{-1} x^2}{1+x^4} d x$
Question 10
10. (a) $\int \frac{x^3 \sin \left(\tan ^{-1} x^4\right)}{1+x^8} d x$
(b) $\int \frac{1}{x^2 \cos ^2\left(\frac{1}{x}\right)} d x$
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