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1
MHT CET 2024 4th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

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

A
$ x-2 \log |(x+1)|-\frac{1}{x+1}+c$, where $c$ is a constant of integration.
B
$ x-2 \log |(x+1)|-\frac{2}{x+1}+c$, where c is a constant of integration.
C
  $ x-\log |(x+1)|-\frac{2}{x+1}+c$, where $c$ is a constant of integration.
D
$x-\log |(x+1)|-\frac{x}{x+1}+\mathrm{c}$, where c is a constant of integration.
2
MHT CET 2024 4th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

$\int\left(1+x-\frac{1}{x}\right) e^{x+\frac{1}{x}} d x$ equal to

A
$(x+1) e^{x+\frac{1}{x}}+c$, (where $c$ is a constant of integration)
B
$-x e^{x+\frac{1}{x}}+c$, (where $c$ is a constant of integration)
C
$(x-1) e^{x+\frac{1}{x}}+c$, (where $c$ is a constant of integration)
D
$x e^{x+\frac{1}{x}}+c$, (where $c$ is a constant of integration)
3
MHT CET 2024 4th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The value of $\mathrm{I}=\int \frac{x^2}{(\mathrm{a}+\mathrm{bx})^2} \mathrm{dx}$ is

A
$\frac{1}{b^3}\left[a+b x+2 a \log |a+b x|-\frac{a^2}{a+b x}\right]+c$, (where c is the constant of integration)
B
$\frac{1}{b^3}\left[a+b x-2 a \log |a+b x|+\frac{a^2}{a+b x}\right]+c$, (where c is the constant of integration)
C
$\frac{1}{b^3}\left[a+b x-2 a \log |a+b x|-\frac{a^2}{a+b x}\right]+c$, (where c is the constant of integration)
D
$\frac{1}{b^3}\left[a+b x+2 a \log |a+b x|+\frac{a^2}{a+b x}\right]+c$, (where c is the constant of integration)
4
MHT CET 2024 4th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $I=\int e^{\sin \theta}\left(\log \sin \theta+\operatorname{cosec}^2 \theta\right) \cos \theta d \theta$, then $I$ is equal to

A
$\mathrm{e}^{\sin \theta}\left(\log \sin \theta+\operatorname{cosec}^2 \theta\right)+\mathrm{c}$, (where c is a constant of integration)
B
$\mathrm{e}^{\sin \theta}(\log \sin \theta+\operatorname{cosec} \theta)+\mathrm{c}$, (where c is a constant of integration)
C
$\mathrm{e}^{\sin \theta}(\log \sin \theta-\operatorname{cosec} \theta)+\mathrm{c}$, (where c is a constant of integration)
D
$\mathrm{e}^{\sin \theta}\left(\log \sin \theta-\operatorname{cosec}^2 \theta\right)+\mathrm{c}$, (where c is a constant of integration)
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