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

$\int \frac{\mathrm{d} x}{x\left(x^3+1\right)}=$

A
$\quad \log \left(\frac{x^3}{x^3+1}\right)+\mathrm{c}$, where c is the constant of integration
B
$\frac{1}{3} \log \left(\sqrt[3]{\frac{x^3}{x^3+1}}\right)+\mathrm{c}$, where c is the constant of integration
C
$\quad \log \left(\sqrt[3]{\frac{x^3}{x^3+1}}\right)+\mathrm{c}$, where c is the constant of integration
D
$\frac{1}{3} \log \left(\frac{x^3+1}{x^3}\right)+\mathrm{c}$, where c is the constant of integration
2
MHT CET 2025 25th April Evening Shift
MCQ (Single Correct Answer)
+2
-0

$\int \frac{x^4 \cos \left(\tan ^{-1} x^5\right)}{1+x^{10}} d x$ equals

A

$\frac{\sin \left(\tan ^{-1} x^5\right)}{5}+\mathrm{c}$, where c is the constant of integration

B

$\quad x^4 \sin \left(\tan ^{-1} x^5\right)+\mathrm{c}$, where c is the constant of integration

C

$\frac{\sin \left(\tan ^{-1} x^5\right)}{4}+\mathrm{c}$, where c is the constant of integration

D

$\quad \cos \left(\tan ^{-1} x^5\right)+\mathrm{c}$, where c is the constant of integration

3
MHT CET 2025 25th April Morning Shift
MCQ (Single Correct Answer)
+2
-0

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

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.
4
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.
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