MHT CET 2024 10th May Morning Shift | Indefinite Integration Question 29 | Mathematics

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

$\frac{46}{5}$

$\frac{16}{15}$

$\frac{24}{5}$

$\frac{13}{15}$

MHT CET 2024 10th May Morning Shift

MCQ (Single Correct Answer)

-0

$$\int \frac{\sqrt{x}}{x+1} d x=$$

$\left(2 \sqrt{x}-\tan ^{-1} \sqrt{x}\right)+\mathrm{c}$, where c is a constant of integration.

$2\left(\sqrt{x}-\tan ^{-1} \sqrt{x}\right)+\mathrm{c}$, where c is a constant of integration.

$\left(2 \sqrt{x}+\tan ^{-1} \sqrt{x}\right)+\mathrm{c}$, where c is a constant of integration.

$2\left(\sqrt{x}+\tan ^{-1} \sqrt{x}\right)+\mathrm{c}$, where c is a constant of integration.

MHT CET 2024 10th May Morning Shift

MCQ (Single Correct Answer)

-0

$$\int \frac{1+\sin (\log x)}{1+\cos (\log x)} d x=$$

$x^2 \tan \left(\frac{\log x}{2}\right)+c$, where $c$ is a constant of integration.

$x \tan \left(\log \left(\frac{x}{2}\right)\right)+\mathrm{c}$, where c is a constant of integration.

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

$x \cdot \tan \left(\frac{\log x}{2}\right)+\mathrm{c}$, where c is a constant of integration.

MHT CET 2024 9th May Evening Shift

MCQ (Single Correct Answer)

-0

The value of $\int \frac{x+1}{x\left(1+x \mathrm{e}^x\right)^2} \mathrm{dx}$ is equal to

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

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

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

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

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