प्रश्नावली - 7F
Question 1
10. (a) $\int \frac{x^3 \sin \left(\tan ^{-1} x^4\right)}{1+x^8} d x$
(b) $\int \frac{1}{x^2 \cos ^2\left(\frac{1}{x}\right)} d x$
(c) $\int \frac{x}{9-4 x^2} d x$
(d) $\int \frac{e^{\sqrt{x}}}{\sqrt{x}} d x$
Question 2
2. (a) $\int \frac{e^{a \tan ^{-1} x}}{1+x^2} d x$
(b) $\int \frac{e^{\tan ^{-1} x}}{1+x^2} d x$
(c) $\int \frac{e^{\cos ^{-1} x}}{\sqrt{1-x^2}} d x$
(d) $\int \frac{e^{m \sec ^{-1} x}}{x \sqrt{x^2-1}} d x$
Question 3
3. (a) $\int \frac{\sec x \operatorname{cosec} x}{\log \cot x} d x$
(b) $\int \frac{\sec ^2\left(\log _e x\right)}{x} d x$
(c) $\int \frac{(x+1)(x+\log x)^2}{x} d x$
(d) $\int \frac{\sin x}{\sin (x-\alpha)} d x$
Question 4
4. (a) $\int \frac{e^{2 x}-1}{e^{2 x}+1} d x$
(b) $\int \frac{\log _e \sqrt{x+1}}{x+1} d x$
Question 5
5. (a) $\int \frac{\sin \left(\tan ^{-1} x\right)}{1+x^2} d x$
(b) $\int \frac{d x}{1-\tan x}$
Question 6
6. (a) $\int \frac{\sec ^2 x d x}{\sqrt{\tan x}}$
(b) $\int \frac{1}{x \sqrt{1+\log _e x}} d x$
Question 7
7. (a) $\int \frac{\operatorname{cosec}^2 x}{1+\cot x} d x$
(b) $\int \frac{\sin x}{1+\cos x} d x$
(c) $\int \frac{\sin \sqrt{x}}{\sqrt{x}} d x$
(d) $\int \frac{\sin x}{(1+\cos x)^2} d x$
Question 8
8. $\int \frac{d x}{e^x+1}$
Question 9
9. $\int \frac{\cos x}{\sqrt{1+\sin x}} d x$
Question 10
10. $\int \tan x \sec ^2 x \sqrt{1-\tan ^2 x} d x$
Question 11
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