MHT CET 2025 26th April Morning Shift | Indefinite Integration Question 1 | Mathematics

If $\int \frac{\left(x^4+1\right)}{x\left(x^2+1\right)^2} d x=A \log |x|+\frac{B}{1+x^2}+c$, then $\mathrm{A}-\mathrm{B}$ is (where c is the constant of integration)

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MHT CET 2025 26th April Morning Shift

MCQ (Single Correct Answer)

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If $\int \frac{\mathrm{d} x}{x^4+5 x^2+4}=\mathrm{A} \tan ^{-1} x+\mathrm{B} \tan ^{-1} \frac{x}{2}+\mathrm{c}$ where c is a constant of integration, then

$\mathrm{A}=\frac{1}{2}, \mathrm{~B}=\frac{1}{4}$

$\mathrm{A}=\frac{1}{3}, \mathrm{~B}=-\frac{1}{6}$

$\mathrm{A}=\frac{1}{3}, \mathrm{~B}=\frac{1}{6}$

$\quad \mathrm{A}=\frac{1}{2}, \mathrm{~B}=-\frac{1}{4}$

MHT CET 2025 26th April Morning Shift

MCQ (Single Correct Answer)

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$$ \int \frac{\sqrt{\tan x}}{\sin x \cdot \cos x} d x= $$

$2 \sqrt{\sec x}+c$, where c is a constant of integration

$2 \sqrt{\tan x}+c$, where $c$ is a constant of integration

$\frac{2}{\sqrt{\tan x}}+\mathrm{c}$, where c is a constant of integration

$\frac{2}{\sqrt{\sec x}}+\mathrm{c}$, where c is a constant of integration

MHT CET 2025 25th April Evening Shift

MCQ (Single Correct Answer)

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$$ \int \frac{\mathrm{d} x}{(x+\mathrm{a})^{\frac{9}{7}}(x-\mathrm{b})^{\frac{5}{7}}}= $$

$\frac{7}{\mathrm{a}+\mathrm{b}}\left(\frac{x-\mathrm{b}}{x+\mathrm{a}}\right)^{\frac{9}{7}}+\mathrm{c}$, where c is the constant of integration.

$\frac{7}{a+b}\left(\frac{x-b}{x+a}\right)^{\frac{5}{7}}+c$, where $c$ is the constant of integration.

$\frac{7}{2(a+b)}\left(\frac{x-b}{x+a}\right)^{\frac{2}{7}}+c$, where $c$ is the constant of integration.

$\frac{7}{a+b}\left(\frac{x-b}{x+a}\right)^{\frac{1}{7}}+c$, where $c$ is the constant of integration.

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