1
MHT CET 2023 9th May Morning Shift
+2
-0

$$\int \frac{1}{\sin (x-a) \sin x} d x=$$

A
$$\sin \mathrm{a}(\log (\sin (x-\mathrm{a}) \cdot \operatorname{cosec} x))+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.
B
$$\operatorname{cosec} a(\log (\sin (x-a) \cdot \operatorname{cosec} x))+c$$, where $$\mathrm{c}$$ is a constant of integration.
C
$$-\sin \mathrm{a}(\log (\sin (x-\mathrm{a}) \cdot \sin x))+\mathrm{c}$$, where c is a constant of integration.
D
$$-\operatorname{cosec} \mathrm{a}(\log (\sin (x-\mathrm{a}) \cdot \sin x))+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.
2
MHT CET 2021 21th September Evening Shift
+2
-0

$$\int \frac{1}{x^{\frac{1}{2}}+x^{\frac{1}{3}}} d x=$$

A
$$\sqrt{\mathrm{x}}-\sqrt[3]{\mathrm{x}}+\sqrt[6]{\mathrm{x}}-\log |\sqrt[6]{\mathrm{x}}+1|+c$$
B
$$2 \sqrt{\mathrm{x}}-3 \sqrt[3]{\mathrm{x}}+6 \sqrt[6]{\mathrm{x}}-6 \log |\sqrt[6]{\mathrm{x}}+1|+\mathrm{c}$$
C
$$2 \sqrt{\mathrm{x}}+3 \sqrt[3]{\mathrm{x}}+6 \sqrt[6]{\mathrm{x}}+6 \log |\sqrt[6]{\mathrm{x}}+1|+c$$
D
$$\sqrt{\mathrm{x}}+\sqrt[3]{\mathrm{x}}+\sqrt[6]{\mathrm{x}}+\log |\sqrt[6]{\mathrm{x}}+1|+\mathrm{c}$$
3
MHT CET 2021 21th September Evening Shift
+2
-0

$$\int[\sin |\log x|+\cos |\log x|] d x=$$

A
$$\sin |\log x|+c$$
B
$$x \cos |\log x|+c$$
C
$$\cos |\log x|+c$$
D
$$x \sin |\log x|+c$$
4
MHT CET 2021 21th September Evening Shift
+2
-0

If $$\int {{{5\tan x} \over {\tan x - 2}}dx = x + a\log |\sin x - 2\cos x| + c}$$, then a = (Where c is constant of integration)

A
1
B
$$-$$2
C
$$-$$1
D
2
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