1
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

2
MHT CET 2025 20th April Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$ \int \log (2+x)^{2+x} d x= $$

A
$\frac{(2+x)^2}{2} \log \left(\frac{2+x}{\sqrt{\mathrm{e}}}\right)+\mathrm{c}$, where c is the constant of integration
B
$\frac{(2+x)^2}{2} \log \left(\frac{2+x}{\mathrm{e}}\right)+\mathrm{c}$, where c is the constant of integration
C
$\frac{2+x}{2} \log \left(\frac{2+x}{\sqrt{\mathrm{e}}}\right)+\mathrm{c}$, where c is the constant of integration
D
$\frac{2+x}{2} \log (2+x) \sqrt{\mathrm{e}}+\mathrm{c}$, where c is the constant of integration
3
MHT CET 2025 20th April Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$ \int \frac{\mathrm{e}^{\tan ^{-1} 2 x}}{1+4 x^2}= $$

A
$4 \mathrm{e}^{\tan ^{-1} 2 x}+\mathrm{c}$, where c is the constant of integration
B
$\mathrm{e}^{\tan ^{-1} 2 x}+\mathrm{c}$, where c is the constant of integration
C
$\frac{\mathrm{e}^{\tan ^{-1} 2 x}}{2}+\mathrm{c}$, where c is the constant of integration
D
$2 \mathrm{e}^{\tan ^{-1} 2 x}+\mathrm{c}$, where c is the constant of integration
4
MHT CET 2025 20th April Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$ \int \mathrm{e}^x \frac{(x-1)}{(x+1)^3} \mathrm{~d} x= $$

A
$\mathrm{e}^x(x+1)^2+\mathrm{c}$, where c is the constant of integration
B
$\mathrm{e}^x(x+1)^3+\mathrm{c}$, where c is the constant of integration
C
$\frac{\mathrm{e}^x}{(x+1)^2}+\mathrm{c}$, where c is the constant of integration
D
$\frac{\mathrm{e}^x}{(x+1)^3}+\mathrm{c}$, where c is the constant of integration
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