MHT CET 2023 12th May Evening Shift | Indefinite Integration Question 94 | Mathematics

If $$\int \frac{\sqrt{1-x^2}}{x^4} \mathrm{~d} x=\mathrm{A}(x)\left(\sqrt{1-x^2}\right)^{\mathrm{m}}+\mathrm{c}$$ for a suitable chosen integer $$\mathrm{m}$$ and a function $$\mathrm{A}(x)$$, where $$\mathrm{c}$$ is a constant of integration, then $$(\mathrm{A}(x))^{\mathrm{m}}$$ equals

$$\frac{1}{9 x^4}$$

$$\frac{-1}{3 x^3}$$

$$\frac{-1}{27 x^9}$$

$$\frac{1}{27 x^6}$$

MHT CET 2023 12th May Evening Shift

MCQ (Single Correct Answer)

-0

$$\int\left(\frac{\tan \left(\frac{1}{x}\right)}{x}\right)^2 d x=$$

$$x-\tan x+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration

$$\frac{1}{x}-\tan \left(\frac{1}{x}\right)+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.

$$\frac{1}{x}+\tan \left(\frac{1}{x}\right)+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.

$$x+\tan x+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.

MHT CET 2023 12th May Evening Shift

MCQ (Single Correct Answer)

-0

$$\int \frac{1}{(x+2)(1+x)^2} d x$$ has the value

$$2 \log \left(\frac{x+2}{x^2+1}\right)+4 \tan ^{-1} x+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.

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

$$\log \frac{(x+2)^2}{\left(x^2+1\right)}+4 \tan ^{-1} x+c$$, where c is a constant of integration.

None

MHT CET 2023 12th May Morning Shift

MCQ (Single Correct Answer)

-0

$$\int \frac{\operatorname{cosec} x d x}{\cos ^2\left(1+\log \tan \frac{x}{2}\right)}=$$

$$\tan \left(1+\log \left(\tan \frac{x}{2}\right)\right)+\mathrm{c}$$, where $$\mathrm{c}$$ is constant of integration

$$\tan (1+\log (\tan x))+c$$, where $$\mathrm{c}$$ is constant of integration

$$\tan \left(\log \left(\tan \frac{x}{2}\right)\right)+c$$, where c is constant of integration.

$$\tan \left(\tan \frac{x}{2}\right)+c$$, where c is constant of integration.

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