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1
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.
2
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
3
MHT CET 2025 23rd April Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$ \int \frac{x}{1+x^4} d x= $$

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

$$ \int \sqrt{x^2+3 x} d x= $$

A

$\sqrt{x^2+3 x}+\log \sqrt{x^2+3 x}+c$, where c is the constant of integration.

B

$\frac{2 x+3}{4} \sqrt{x^2+3 x}-\frac{9}{8} \log \left(x+\sqrt{x^2+3 x}\right)+c$, where c is the constant of integration.

C

$x \sqrt{x^2+3 x}+\log \left(x+\sqrt{x^2+3 x}\right)+\mathrm{c}$, where c is the constant of integration.

D

$x+3 \sqrt{x^2+3 x}+\frac{3}{2} \log \left(x+\sqrt{x^2+3 x}\right)+\mathrm{c}$, where c is the constant of integration.

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