MHT CET 2023 10th May Evening Shift | Indefinite Integration Question 34 | Mathematics

$$\int \frac{5 \tan x}{\tan x-2} \mathrm{~d} x=x+\mathrm{a} \log |\sin x-2 \cos x|+\mathrm{c},$$ (where $$c$$ is a constant of integration), then the value of $$a$$ is

$$\frac{1}{2}$$

MHT CET 2023 10th May Evening Shift

MCQ (Single Correct Answer)

-0

The value of $$\int \frac{\left(x^2-1\right) d x}{x^3 \sqrt{2 x^4-2 x^2+1}}$$ is

$$2 \sqrt{2-\frac{2}{x^2}+\frac{1}{x^4}}+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.

$$2 \sqrt{2+\frac{2}{x^2}+\frac{1}{x^4}}+c$$, where $$\mathrm{c}$$ is a constant of integration.

$$\frac{1}{2} \sqrt{2-\frac{2}{x^2}+\frac{1}{x^4}}+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.

$$2 \sqrt{2-\frac{2}{x^2}-\frac{1}{x^4}}+c$$, where $$\mathrm{c}$$ is a constant of integration.

MHT CET 2023 10th May Evening Shift

MCQ (Single Correct Answer)

-0

$$\int \mathrm{e}^x\left(1-\cot x+\cot ^2 x\right) \mathrm{d} x=$$

$$\mathrm{e}^x \cdot \cot x+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.

$$\mathrm{e}^x \cdot \operatorname{cosec} x+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.

$$-\mathrm{e}^x \cdot \cot x+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.

$$-\mathrm{e}^x \cdot \operatorname{cosec} x+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.

MHT CET 2023 10th May Morning Shift

MCQ (Single Correct Answer)

-0

If $$\int \sqrt{\frac{x-7}{x-9}} d x=A \sqrt{x^2-16 x+63}+\log \left|(x-8)+\sqrt{x^2-16 x+63}\right|+c,$$

(where $$\mathrm{c}$$ is a constant of integration) then $$\mathrm{A}$$ is

$$-1$$

$$\frac{1}{2}$$

$$1$$

$$\frac{-1}{2}$$

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