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MHT CET 2025 20th April Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$ \int \log (2+x)^{2+x} d x= $$

A
$\frac{(2+x)^2}{2} \log \left(\frac{2+x}{\sqrt{\mathrm{e}}}\right)+\mathrm{c}$, where c is the constant of integration
B
$\frac{(2+x)^2}{2} \log \left(\frac{2+x}{\mathrm{e}}\right)+\mathrm{c}$, where c is the constant of integration
C
$\frac{2+x}{2} \log \left(\frac{2+x}{\sqrt{\mathrm{e}}}\right)+\mathrm{c}$, where c is the constant of integration
D
$\frac{2+x}{2} \log (2+x) \sqrt{\mathrm{e}}+\mathrm{c}$, where c is the constant of integration
2
MHT CET 2025 20th April Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$ \int \frac{\mathrm{e}^{\tan ^{-1} 2 x}}{1+4 x^2}= $$

A
$4 \mathrm{e}^{\tan ^{-1} 2 x}+\mathrm{c}$, where c is the constant of integration
B
$\mathrm{e}^{\tan ^{-1} 2 x}+\mathrm{c}$, where c is the constant of integration
C
$\frac{\mathrm{e}^{\tan ^{-1} 2 x}}{2}+\mathrm{c}$, where c is the constant of integration
D
$2 \mathrm{e}^{\tan ^{-1} 2 x}+\mathrm{c}$, where c is the constant of integration
3
MHT CET 2025 20th April Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$ \int \mathrm{e}^x \frac{(x-1)}{(x+1)^3} \mathrm{~d} x= $$

A
$\mathrm{e}^x(x+1)^2+\mathrm{c}$, where c is the constant of integration
B
$\mathrm{e}^x(x+1)^3+\mathrm{c}$, where c is the constant of integration
C
$\frac{\mathrm{e}^x}{(x+1)^2}+\mathrm{c}$, where c is the constant of integration
D
$\frac{\mathrm{e}^x}{(x+1)^3}+\mathrm{c}$, where c is the constant of integration
4
MHT CET 2025 20th April Morning Shift
MCQ (Single Correct Answer)
+2
-0

$$ \int \sin ^5 x \mathrm{~d} x= $$

A
$\cos x+\frac{2}{3} \cos ^2 x-\frac{\cos ^5 x}{5}+\mathrm{c}$, where c is the constant of integration
B
$\quad \cos x+\frac{2}{3} \cos ^2 x+\frac{\cos ^5 x}{5}+\mathrm{c}$, where c is the constant of integration
C
$-\left(\cos x-\frac{2}{3} \cos ^2 x+\frac{\cos ^5 x}{5}+\mathrm{c}\right)$, where c is the constant of integration
D
$\cos x-\frac{2}{3} \cos ^2 x+\frac{\cos ^5 x}{5}+\mathrm{c}$, where c is the constant of integration
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Functions Limits, Continuity and Differentiability Differentiation Application of Derivatives Indefinite Integration Definite Integration Area Under The Curves Differential Equations
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Straight Lines and Pair of Straight Lines Circle Parabola Ellipse Hyperbola
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