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

$$ \int\left(\frac{x-3}{x^2+9}\right)^2 d x= $$

A
$\frac{1}{3} \tan ^{-1}\left(\frac{x}{3}\right)-\frac{3}{x^2+9}+\mathrm{c}$, where c is the constant of integration.
B
$\frac{1}{3} \tan ^{-1}\left(\frac{x}{3}\right)-\frac{1}{x^2+9}+c$, where $c$ is the constant of integration.
C
$\frac{1}{3} \tan ^{-1}\left(\frac{x}{3}\right)+\frac{3}{x^2+9}+c$, where $c$ is the constant of integration.
D
$\frac{1}{3} \tan ^{-1}\left(\frac{x}{3}\right)-\frac{1}{x^2+9}+c$, where $c$ is the constant of integration.
3
MHT CET 2025 22nd April Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$ \int \frac{x^3}{x^4+5 x^2+4} d x= $$

A

$\frac{1}{3} \log \left(\frac{\left(x^2+4\right)^2}{\sqrt{x^2+1}}\right)+\mathrm{c}$, where c is the constant of integration

B
$\quad \log \left(\frac{\left(x^2+4\right)^2}{\sqrt{x^2+1}}\right)+\mathrm{c}$, where c is the constant of integration
C
$3 \log \left(\frac{\left(x^2+4\right)^2}{\sqrt{x^2+1}}\right)+\mathrm{c}$, where c is the constant of integration
D
$\frac{2}{3} \log \left(\frac{\left(x^2+4\right)^2}{\sqrt{x^2+1}}\right)+\mathrm{c}$, where c is the constant of integration
4
MHT CET 2025 22nd April Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$ \int \sec ^{\frac{2}{3}} x \cdot \operatorname{cosec}^{\frac{4}{3}} x d x= $$

A
$3 \tan ^{\frac{-1}{3}} x+\mathrm{c}$, where c is the constant of integration
B
$-3 \tan ^{\frac{-1}{3}} x+c$, where $c$ is the constant of integration
C
$-3 \cot ^{\frac{-1}{3}} x+c$, where $c$ is the constant of integration
D
$-\frac{3}{4} \tan ^{\frac{-4}{3}} x+\mathrm{c}$, where c is the constant of integration
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