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1
MHT CET 2024 15th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The value of $\int \frac{d x}{5+4 \sin x}$ is equal to

A
$\frac{2}{5} \tan ^{-1}\left(\frac{5 \tan \frac{x}{2}+4}{3}\right)+\mathrm{c}$, (where c is a constant of integration)
B
$\frac{2}{3} \tan ^{-1}\left(\frac{5 \tan \frac{x}{2}+4}{3}\right)+\mathrm{c}$, (where c is a constant of integration)
C
$\frac{2}{5} \log \left(\frac{5 \tan \frac{x}{2}+7}{5 \tan \frac{x}{2}+1}\right)+\mathrm{c}$, (where c is a constant of integration)
D
$\frac{2}{3} \log \left(\frac{5 \tan \frac{x}{2}+7}{5 \tan \frac{x}{2}+1}\right)+\mathrm{c}$, (where c is a constant of integration)
2
MHT CET 2024 11th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\int \frac{x+1}{x\left(1+x \mathrm{e}^x\right)^2} \mathrm{dx}=$$

A
$\log \left|\frac{x \mathrm{e}^x}{1+x \mathrm{e}^x}\right|+\frac{x}{1+x \mathrm{e}^x}+c$, (where c is a constant of integration)
B
$\quad \log \left|\frac{x \mathrm{e}^x}{1+x \mathrm{e}^x}\right|+\frac{\mathrm{e}^x}{1+x \mathrm{e}^x}+c$, (where c is a constant of integration)
C
$\quad \log \left|\frac{x \mathrm{e}^x}{1+x \mathrm{e}^x}\right|+\frac{1}{1+x \mathrm{e}^x}+c$, (where c is a constant of integration)
D
$\log \left|\frac{x \mathrm{e}^x}{1+x \mathrm{e}^x}\right|-\frac{1}{1+x \mathrm{e}^x}+c$, (where c is a constant of integration)
3
MHT CET 2024 11th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $\mathrm{f}(x)=1+x ; \mathrm{g}(x)=\log x$, then $\int \mathrm{g}(\mathrm{f}(x)) \mathrm{d} x$ is equal to

A
$(1+x) \log (1+x)-x+\mathrm{c}$, (where c is a constant of integration)
B
$(1+x) \log x-x+\mathrm{c}$, (where c is a constant of integration)
C
$x \log (1+x)+c$, (where c is a constant of integration)
D
$(1+x) \log (1+x)+x+\mathrm{c}$, (where c is a constant of integration)
4
MHT CET 2024 11th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\int \cos (\log x) \mathrm{d} x=$$

A
$\frac{x}{2}(\sin (\log x)-\cos (\log x))+c$, (where c is a constant of integration)
B
$x(\cos (\log x)-\sin (\log x))+c$, (where c is a constant of integration)
C
$\frac{x}{2}(\cos (\log x)+\sin (\log x))+\mathrm{c}$, (where c is a constant of integration)
D
$x(\cos (\log x)+\sin (\log x))+c$, (where c is a constant of integration)
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