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1
MHT CET 2025 25th April Morning Shift
MCQ (Single Correct Answer)
+2
-0

$$ \int \frac{1}{\mathrm{e}^x+1} \mathrm{~d} x= $$

A
$x+\log \left(\mathrm{e}^x+1\right)+\mathrm{c}$, where c is the constant of integration.
B
$x-\log \left(\mathrm{e}^x+1\right)+\mathrm{c}$, where c is the constant of integration.
C
$\log \left(\mathrm{e}^x-1\right)+x+\mathrm{c}$, where c is the constant of integration.
D
$\log \left(\mathrm{e}^{\mathrm{x}}-1\right)-x+\mathrm{c}$, where c is the constant of integration.
2
MHT CET 2025 25th April Morning Shift
MCQ (Single Correct Answer)
+2
-0

$\int \mathrm{e}^x\left(\frac{x+5}{(x+6)^2}\right) \mathrm{d} x$ is

A
$\frac{\mathrm{e}^x}{(x+6)^2}+\mathrm{c}$, where c is the constant of integration.
B
$\frac{\mathrm{e}^x}{x+5}+\mathrm{c}$, where c is the constant of integration.
C
$\frac{\mathrm{e}^x}{(x+5)^2}+\mathrm{c}$, where c is the constant of integration.
D
$\frac{\mathrm{e}^x}{x+6}+\mathrm{c}$, where c is the constant of integration.
3
MHT CET 2025 25th April Morning Shift
MCQ (Single Correct Answer)
+2
-0

$\int \frac{\mathrm{d} x}{3 \cos 2 x+5}$ equals

A
$\frac{1}{2} \tan ^{-1}(\tan x)+\mathrm{c}$, where c is the constant of integration.
B
$\frac{1}{2} \tan ^{-1}\left(\frac{\tan x}{2}\right)+\mathrm{c}$, where c is the constant of integration.
C
$\frac{1}{4} \tan ^{-1}\left(\frac{1}{2} \tan x\right)+\mathrm{c}$, where c is the constant of integration.
D
$\frac{1}{4} \tan ^{-1}(\tan x)+\mathrm{c}$, where c is the constant of integration.
4
MHT CET 2025 23rd April Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$ \int \frac{(5 \sin \theta-2) \cos \theta}{\left(5-\cos ^2 \theta-4 \sin \theta\right)} d \theta= $$

A
$(\log 5 \sin \theta-2)+\mathrm{c}$, where c is the constant of integration
B
$5 \log (5 \sin \theta-2)-\frac{8}{(\sin \theta-2)}+\mathrm{c}$, where c is the constant of integration
C
$\log (5 \sin \theta-2)+\frac{8}{(\sin \theta-2)}+c$, where $c$ is the constant of integration
D
$\log (5 \sin \theta-2)+\frac{1}{(\sin \theta-2)}+c$, where $c$ is the constant of integration
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