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1
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
2
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.

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

$$ \int \frac{\mathrm{d} x}{\sqrt{x}+x}= $$

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

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

A
$\quad \log \left(\mathrm{e}^{\mathrm{x}}-1\right)+x+\mathrm{c}$, where c is the constant of integration.
B
$\quad \log \left(\mathrm{e}^{\mathrm{x}}-1\right)-x+\mathrm{c}$, where c is the constant of integration.
C
$\quad x-\log \left(\mathrm{e}^x-1\right)+\mathrm{c}$, where c is the constant of integration.
D
$\log \left(\mathrm{e}^{\mathrm{x}}-1\right)-x \mathrm{e}^{\mathrm{x}}+\mathrm{c}$, where c is the constant of integration.
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