MHT CET 2024 2nd May Evening Shift | Indefinite Integration Question 56 | Mathematics

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

$\frac{1}{3}(x+1)$

$\frac{1}{3}(x+4)$

$\frac{2}{3}(x+2)$

$\frac{2}{3}(x-4)$

MHT CET 2024 2nd May Evening Shift

MCQ (Single Correct Answer)

-0

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

$-\left(x^4+1\right)^{\frac{1}{4}}+\mathrm{c}$, (where c is a constant of integration)

$\left(x^4+1\right)^{\frac{1}{4}}+\mathrm{c},($ where c is a constant of integration)

$\left(1+\frac{1}{x^4}\right)^{\frac{1}{4}}+\mathrm{c}$, (where c is a constant of integration)

$-\left(1+\frac{1}{x^4}\right)^{\frac{1}{4}}+\mathrm{c}$, (where c is a constant of integration)

MHT CET 2024 2nd May Evening Shift

MCQ (Single Correct Answer)

-0

$\int\left(\mathrm{f}(x) \mathrm{g}^{\prime \prime}(x)-\mathrm{f}^{\prime \prime}(x) \mathrm{g}(x)\right) \mathrm{d} x$ is equal to

$\mathrm{f}(x) \mathrm{g}(x)-\mathrm{f}^{\prime}(x) \mathrm{g}^{\prime}(x)$

$\mathrm{f}^{\prime}(x) \mathrm{g}(x)-\mathrm{f}(x) \mathrm{g}^{\prime}(x)$

$\mathrm{f}(x) \mathrm{g}^{\prime}(x)-\mathrm{f}^{\prime}(x) \mathrm{g}(x)$

$\mathrm{f}(x) \mathrm{g}^{\prime}(x)+\mathrm{f}^{\prime}(x) \mathrm{g}(x)$

MHT CET 2024 2nd May Evening Shift

MCQ (Single Correct Answer)

-0

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

$\frac{1}{3}(\log \sqrt{x})+\mathrm{c}$, (where $c$ is a constant of integration)

$\frac{2}{3}(\log \sqrt{x})^2+\mathrm{c}$, (where c is a constant of integration)

$\frac{2}{3}(\log x)^2+\mathrm{c}$, (where c is a constant of integration)

$\frac{1}{12}(\log x)^2+\mathrm{c},($ where c is a constant of integration)

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