MHT CET 2025 19th April Evening Shift | Indefinite Integration Question 5 | 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 2024 16th May Evening Shift

MCQ (Single Correct Answer)

-0

$\int \frac{x^2-4}{x^4+9 x^2+16} \mathrm{dx}=\tan ^{-1}(\mathrm{f}(x))+\mathrm{c}$ (where c is a constant of integration), then value of $f(2)$ is

MHT CET 2024 16th May Evening Shift

MCQ (Single Correct Answer)

-0

$$\int \cos ^{\frac{-3}{7}} x \cdot \sin ^{\frac{-11}{7}} x d x=$$

$\frac{-4}{7} \tan ^{\frac{-4}{7}} x+c$, where $c$ is a constant of integration.

$\frac{4}{7} \tan ^{\frac{4}{7}} x+c$, where c is a constant of integration.

$\frac{-7}{4} \tan ^{\frac{-4}{7}} x+c$, where c is a constant of integration.

$\frac{7}{4} \tan ^{\frac{4}{7}} x+c$, where c is a constant of integration.

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