प्रश्नावली - 7I
Question 1
निम्नलिखित का मान ज्ञात कीजिए-
1. (a) $\int \frac{d x}{4+x^2}$
(b) $\int \frac{d x}{5+4 x^2}$
(c) $\int \frac{3 x^2}{x^6+1} d x$
(d) $\int \frac{x^2 d x}{4+x^2}$
Question 2
2. (a) $\int \frac{d x}{\sqrt{4-9 x^2}}$
(b) $\int \frac{d x}{\sqrt{1+4 x^2}}$
(c) $\int \frac{d x}{x \sqrt{x^2-4}}$
(d) $\int \frac{d x}{\sqrt{9-25 x^2}}$
Question 3
(a) $\int \frac{d x}{\sqrt{(2-x)^2+1}}$
(b) $\int \frac{x^2 d x}{\sqrt{a^6+x^6}}$
(c) $\int \frac{e^x d x}{\sqrt{4+e^{2 x}}}$
(d) $\int \frac{x-1}{\sqrt{x^2+1}} d x$
Question 4
4. (a) $\int \frac{d x}{e^x+e^{-x}}$
(b) $\int \frac{d x}{\sqrt{1-e^{2 x}}}$
(c) $\int \frac{a^x d x}{\sqrt{1-a^{2 x}}}$
Question 5
5. $\int \frac{d x}{x^2\left(x^4+1\right)^{3 / 4}}$
Question 6
6. $\int \sqrt{\frac{1+x}{1-x}} d x$
Question 7
7. (i) $\int \cos ^3 x e^{\log \sin x} d x$
(ii) $\int e^{3 \log x}\left(x^4+1\right)^{-1} d x$
Question 8
निम्नलिखित का मान ज्ञात कीजिए-
8. $\int \sqrt{\frac{a-x}{a+x}} d x$
Question 9
9 .
(a) $\int \frac{e^x-\sin x}{e^x+\cos x} d x$
(b) $\int f^{\prime}(a x+b)[f(a x+b)]^n d x$
Question 10
10. $\int \frac{\sin x d x}{1+\cos ^2 x}$
Question 11
11. (i) $\int \frac{d x}{\sqrt{\sin ^3 x \sin (x+\alpha)}}$
(ii) $\int \frac{2+\sin 2 x}{1+\cos 2 x} e^x d x$
Question 12
12. $\int \frac{x d x}{a^4+x^4}$
Question 13
13. $\int \frac{1}{\left(1+x^2\right) \sqrt{p^2+q^2\left(\tan ^{-1} x\right)^2}} d x$
Question 14
14. (i) $\int \frac{\sin ^{-1} \sqrt{x}-\cos ^{-1} \sqrt{x}}{\sin ^{-1} \sqrt{x}+\cos ^{-1} \sqrt{x}} d x$
(ii) $\int \sqrt{\frac{1-\sqrt{x}}{1+\sqrt{x}}} d x$
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