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1
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
2
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
3
MHT CET 2025 22nd April Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$ \int \mathrm{e}^{2 x} \frac{(\sin 2 x \cos 2 x-1)}{\sin ^2 2 x} \mathrm{~d} x= $$

A
$\mathrm{e}^{2 x} \cot (2 x)+\mathrm{c}$, where c is the constant of integration
B
$2 \mathrm{e}^{2 x} \cot (2 x)+\mathrm{c}$, where c is the constant of integration
C
$4 \mathrm{e}^{2 x} \cot (2 x)+\mathrm{c}$, where c is the constant of integration
D
$\frac{1}{2} \mathrm{e}^{2 x} \cot (2 x)+\mathrm{c}$, where c is the constant of integration
4
MHT CET 2025 22nd April Morning Shift
MCQ (Single Correct Answer)
+2
-0

$$ \int \frac{\sin 2 x \cos 2 x}{\sqrt{9-\cos ^4 2 x}} d x= $$

A
$\frac{1}{4} \sin ^{-1}\left(\frac{\cos ^2 2 x}{2}\right)+\mathrm{c}$, where c is the constant of integration.
B
$\frac{-1}{4} \sin ^{-1}\left(\frac{\cos ^2 2 x}{2}\right)+\mathrm{c}$, where c is the constant of integration.
C
$\frac{1}{2} \sin ^{-1}\left(\frac{\cos ^2 2 x}{2}\right)+\mathrm{c}$, where c is the constant of integration.
D
$\frac{-1}{2} \sin ^{-1}\left(\frac{\cos ^2 2 x}{2}\right)+\mathrm{c}$, where c is the constant of integration.
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