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1
MHT CET 2024 2nd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$\int \frac{\log \sqrt{x}}{3 x} \mathrm{dx}$ is equal to

A
$\frac{1}{3}(\log \sqrt{x})+\mathrm{c}$, (where $c$ is a constant of integration)
B
$\frac{2}{3}(\log \sqrt{x})^2+\mathrm{c}$, (where c is a constant of integration)
C
$\frac{2}{3}(\log x)^2+\mathrm{c}$, (where c is a constant of integration)
D
$\frac{1}{12}(\log x)^2+\mathrm{c},($ where c is a constant of integration)
2
MHT CET 2024 2nd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

$$\int 3^{3^x} \cdot 3^x d x=$$

A
$\frac{3^x}{(\log 3)^2}+c$, where $c$ is a constant of integration.
B
$\frac{3^{3^x}}{\log 3}+\mathrm{c}$, where c is a constant of integration.
C
$\frac{3^{3^x}}{(\log 3)^2}+c$, where $c$ is a constant of integration.
D
$\frac{3^x}{\log 3}+\mathrm{c}$, where c is a constant of integration.
3
MHT CET 2024 2nd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

$$\int \log (1+x)^{1+x} \mathrm{~d} x=$$

A
$(1+x)^2 \log (1+x)-\frac{1}{2}+\mathrm{c}$, where c is a constant of integration.
B
$\frac{(1+x)^2}{2} \log (1+x)+\mathrm{c}$, where c is a constant of integration.
C
$\frac{(1+x)^2}{2}\left[\log (1+x)-\frac{1}{2}\right]+\mathrm{c}$, where c is a constant of integration.
D
$\frac{1+x}{2} \log (1+x)+\mathrm{c}$, where c is a constant of integration.
4
MHT CET 2024 2nd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

$$\int\left(\frac{x+2}{x+4}\right)^2 \cdot e^x \mathrm{~d} x=$$

A
$\mathrm{e}^x\left(\frac{x}{x+4}\right)+\mathrm{c}$, where c is a constant of integration.
B
$\mathrm{e}^x\left(\frac{x+2}{x+4}\right)+\mathrm{c}$, where c is a constant of integration.
C
$\mathrm{e}^x\left(\frac{x-2}{x+4}\right)+\mathrm{c}$, where c is a constant of integration.
D
$\mathrm{e}^x\left(\frac{2 x}{x+4}\right)+\mathrm{c}$, where c is a constant of integration.
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