MHT CET 2023 9th May Morning Shift | Indefinite Integration Question 14 | Mathematics

If $$ I=\int \frac{\sin x+\sin ^3 x}{\cos 2 x} d x=P \cos x+Q \log \left|\frac{\sqrt{2} \cos x-1}{\sqrt{2} \cos x+1}\right| $$ (where $$c$$ is a constant of integration), then values of $$\mathrm{P}$$ and $$\mathrm{Q}$$ are respectively

$$\frac{1}{2}, \frac{3}{4 \sqrt{2}}$$

$$\frac{1}{2}, \frac{-3}{4 \sqrt{2}}$$

$$\frac{1}{2}, \frac{3}{2 \sqrt{2}}$$

$$\frac{1}{2}, \frac{-3}{2 \sqrt{2}}$$

MHT CET 2023 9th May Morning Shift

MCQ (Single Correct Answer)

-0

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

$$ \sin \mathrm{a}(\log (\sin (x-\mathrm{a}) \cdot \operatorname{cosec} x))+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.

$$\operatorname{cosec} a(\log (\sin (x-a) \cdot \operatorname{cosec} x))+c$$, where $$\mathrm{c}$$ is a constant of integration.

$$-\sin \mathrm{a}(\log (\sin (x-\mathrm{a}) \cdot \sin x))+\mathrm{c}$$, where c is a constant of integration.

$$-\operatorname{cosec} \mathrm{a}(\log (\sin (x-\mathrm{a}) \cdot \sin x))+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.

MHT CET 2021 21th September Evening Shift

MCQ (Single Correct Answer)

-0

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

$$\sqrt{\mathrm{x}}-\sqrt[3]{\mathrm{x}}+\sqrt[6]{\mathrm{x}}-\log |\sqrt[6]{\mathrm{x}}+1|+c$$

$$2 \sqrt{\mathrm{x}}-3 \sqrt[3]{\mathrm{x}}+6 \sqrt[6]{\mathrm{x}}-6 \log |\sqrt[6]{\mathrm{x}}+1|+\mathrm{c}$$

$$2 \sqrt{\mathrm{x}}+3 \sqrt[3]{\mathrm{x}}+6 \sqrt[6]{\mathrm{x}}+6 \log |\sqrt[6]{\mathrm{x}}+1|+c$$

$$\sqrt{\mathrm{x}}+\sqrt[3]{\mathrm{x}}+\sqrt[6]{\mathrm{x}}+\log |\sqrt[6]{\mathrm{x}}+1|+\mathrm{c}$$

MHT CET 2021 21th September Evening Shift

MCQ (Single Correct Answer)

-0

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

$$\sin |\log x|+c$$

$$x \cos |\log x|+c$$

$$\cos |\log x|+c$$

$$x \sin |\log x|+c$$

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