1
MHT CET 2025 21st April Evening Shift
MCQ (Single Correct Answer)
+2
-0

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

A
$\frac{x^2}{2}-2 x+3 \log (x+1)+\frac{1}{x+1}+c$ where c is the constant of integration
B
$\frac{x^2}{2}+2 x-3 \log (x+1)+\frac{1}{x+1}+c$ where c is the constant of integration
C
$\frac{x^2}{2}-2 x+3 \log (x+1)-\frac{1}{x+1}+\mathrm{c}$, where c is the constant of integratio
D
$\frac{x^2}{2}-2 x-3 \log (x+1)-\frac{1}{x+1}+\mathrm{c}$, where c is the constant of integration
2
MHT CET 2025 21st April Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $\quad \int \frac{3 \sin x \cos x}{4 \sin x+7} \mathrm{~d} x=\mathrm{A} \sin x-\mathrm{Blog}(4 \sin x+7)+\mathrm{c}$ where c is the constant of integration, then the value of $\mathrm{A}+\mathrm{B}$ is equal to

A
$\frac{9}{16}$
B
$\frac{-9}{16}$
C
$\frac{33}{16}$
D
$\frac{-33}{16}$
3
MHT CET 2025 21st April Morning Shift
MCQ (Single Correct Answer)
+2
-0

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

A
$\log (x)-\frac{1}{2} \log \left(x^2+1\right)+\mathrm{c}$, where c is the constant of integration.
B
$\frac{1}{2} \log (x)-\log \left(x^2+1\right)+\mathrm{c}$, where c is the constant of integration.
C
$\log (x)+\frac{1}{2} \log \left(x^2+1\right)+\mathrm{c}$, where c is the constant of integration.
D
$-\log (x)-\frac{1}{2} \log \left(x^2+1\right)+\mathrm{c}$, where c is the constant of integration.
4
MHT CET 2025 21st April Morning Shift
MCQ (Single Correct Answer)
+2
-0

$\int \sqrt{x^2-6 x-16} \mathrm{~d} x$ equals

A

$\left(\frac{x-3}{2}\right) \sqrt{x^2-6 x-16} +\frac{5}{2} \log \left(x-3+\sqrt{x^2-6 x-16}\right)+c$

where c is the constant of integration

B

$$ \begin{aligned} & \left(\frac{x-3}{2}\right) \sqrt{x^2-6 x-16} -\frac{25}{2} \log \left(x-3+\sqrt{x^2-6 x-16}\right)+c \end{aligned} $$

where c is the constant of integration

C

$\left(\frac{x-3}{2}\right) \sqrt{x^2-6 x-16}+\frac{25}{2} \log \left(x-3+\sqrt{x^2-6 x-16}\right)+c $

where c is the constant of integration

D

$$ \begin{aligned} \left(\frac{x-3}{2}\right) \sqrt{x^2-6 x-16} & -\frac{5}{2} \log \left(x-3+\sqrt{x^2-6 x-16}\right)+c \end{aligned} $$

where $c$ is the constant of integration

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