1
MHT CET 2024 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $\quad \int(2 x+4) \sqrt{x-1} d x=a(x-1)^{5 / 2}+b(x-1)^{3 / 2}+c$ where $c$ is a constant of integration, then the value of $(2 a+b)$ is

A
$\frac{20}{5}$
B
$\frac{28}{5}$
C
$\frac{48}{5}$
D
$\frac{16}{5}$
2
MHT CET 2024 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The value of $\int \frac{(x-1) \mathrm{e}^x}{(x+1)^3} \mathrm{~d} x$ is equal to

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

If $\int \frac{x+1}{\sqrt{2 x-1}} \mathrm{~d} x=\mathrm{f}(x) \sqrt{2 x-1}+\mathrm{c}$, (where c is a constant of integration), then $\mathrm{f}(x)$ is equal to

A
$\frac{1}{3}(x+1)$
B
$\frac{1}{3}(x+4)$
C
$\frac{2}{3}(x+2)$
D
$\frac{2}{3}(x-4)$
4
MHT CET 2024 2nd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The value of $\mathrm{I}=\int \frac{\mathrm{d} x}{x^2\left(x^4+1\right)^{\frac{3}{4}}}$ is

A
$-\left(x^4+1\right)^{\frac{1}{4}}+\mathrm{c}$, (where c is a constant of integration)
B
$\left(x^4+1\right)^{\frac{1}{4}}+\mathrm{c},($ where c is a constant of integration)
C
$\left(1+\frac{1}{x^4}\right)^{\frac{1}{4}}+\mathrm{c}$, (where c is a constant of integration)
D
$-\left(1+\frac{1}{x^4}\right)^{\frac{1}{4}}+\mathrm{c}$, (where c is a constant of integration)
MHT CET Subjects
EXAM MAP