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1
MHT CET 2023 12th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

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

A
$$2 \log \left(\frac{x+2}{x^2+1}\right)+4 \tan ^{-1} x+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.
B
$$\log \frac{x+2}{x^2+1}-4 \tan ^{-1} x+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.
C
$$\log \frac{(x+2)^2}{\left(x^2+1\right)}+4 \tan ^{-1} x+c$$, where c is a constant of integration.
D
None
2
MHT CET 2023 12th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

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

A
$$\tan \left(1+\log \left(\tan \frac{x}{2}\right)\right)+\mathrm{c}$$, where $$\mathrm{c}$$ is constant of integration
B
$$\tan (1+\log (\tan x))+c$$, where $$\mathrm{c}$$ is constant of integration
C
$$\tan \left(\log \left(\tan \frac{x}{2}\right)\right)+c$$, where c is constant of integration.
D
$$\tan \left(\tan \frac{x}{2}\right)+c$$, where c is constant of integration.
3
MHT CET 2023 12th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The integral $$\int \frac{\sin ^2 x \cos ^2 x}{\left(\sin ^5 x+\cos ^3 x \sin ^2 x+\sin ^3 x \cos ^2 x+\cos ^5 x\right)^2} \mathrm{~d} x$$ is equal to

A
$$\frac{1}{3\left(1+\tan ^3 x\right)}+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.
B
$$\frac{-1}{3\left(1+\tan ^3 x\right)}+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.
C
$$\frac{1}{1+\cot ^3 x}+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.
D
$$\frac{-1}{1+\cos ^3 x}+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.
4
MHT CET 2023 12th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

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

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