MHT CET 2025 19th April Evening Shift | Indefinite Integration Question 38 | Mathematics

If $\int \tan ^4 x \mathrm{~d} x=\mathrm{a} \tan ^3 x+\mathrm{b} \tan x+\mathrm{c} x+\mathrm{k}$ (where k is the constant of integration) then the value of $\mathrm{a}-\mathrm{b}+\mathrm{c}=$

$\frac{7}{3}$

$\frac{5}{3}$

$\frac{4}{3}$

$\frac{1}{3}$

MHT CET 2025 19th April Evening Shift

MCQ (Single Correct Answer)

-0

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

$\log \left(\frac{x-1}{x-2}\right)+\mathrm{c}$, where c is the constant of integration

$\quad \log \left(\frac{x-2}{(x-1)^2}\right)+\mathrm{c}$, where c is the constant of integration

$\log \left(\frac{x-2}{x-1}\right)+\mathrm{c}$, where c is the constant of integration

$\quad \log \left(\frac{(x-2)^2}{x-1}\right)+\mathrm{c}$, where c is the constant of integration

MHT CET 2025 19th April Morning Shift

MCQ (Single Correct Answer)

-0

$$\int \frac{\mathrm{d} x}{2 \mathrm{e}^{2 x}+3 \mathrm{e}^x+1}=$$

$x+\log \left(\mathrm{e}^x+1\right)-2 \log \left(2 \mathrm{e}^x+1\right)+\mathrm{c}$, where c is the constant of integration

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

$x+\log \left(\mathrm{e}^x+1\right)-4 \log \left(2 \mathrm{e}^x+1\right)+\mathrm{c}$, where c is the constant of integration

$x-\log \left(\mathrm{e}^x+1\right)+2 \log \left(2 \mathrm{e}^x+1\right)+\mathrm{c}$, where c is the constant of integration

MHT CET 2025 19th April Morning Shift

MCQ (Single Correct Answer)

-0

$$\int \frac{\mathrm{e}^{2030 \log x}-\mathrm{e}^{2029 \log x}}{\mathrm{e}^{2028 \log x}-\mathrm{e}^{2027 \log x}} \mathrm{~d} x=\ldots$$

$\frac{x^2}{2}+c$, where $c$ is the constant of integration

$x+c$, where $c$ is the constant of integration

$\frac{x^3}{3}+c$, where $c$ is the constant of integration

$\frac{x}{3}+c$, where $c$ is the constant of integration

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