MHT CET 2025 21st April Evening Shift | Indefinite Integration Question 20 | Mathematics

$$ \int \cos \left(\frac{x}{16}\right) \cdot \cos \left(\frac{x}{8}\right) \cdot \cos \left(\frac{x}{4}\right) \cdot \sin \left(\frac{x}{16}\right) \mathrm{d} x= $$

$\frac{\cos 16 x}{256}+\mathrm{c}$, where c is the constant of integration

$\frac{-\cos 16 x}{256}+c$, where $c$ is the constant of integration

$\frac{\sin 16 x}{256}+c$, where $c$ is the constant of integration

$\frac{-\cos \left(\frac{x}{2}\right)}{4}+\mathrm{c}$, where $c$ is the constant of integration

MHT CET 2025 21st April Evening Shift

MCQ (Single Correct Answer)

-0

$$ \int \frac{x^3}{(x+1)^2} d x= $$

$\frac{x^2}{2}-2 x+3 \log (x+1)+\frac{1}{x+1}+c$ where c is the constant of integration

$\frac{x^2}{2}+2 x-3 \log (x+1)+\frac{1}{x+1}+c$ where c is the constant of integration

$\frac{x^2}{2}-2 x+3 \log (x+1)-\frac{1}{x+1}+\mathrm{c}$, where c is the constant of integratio

$\frac{x^2}{2}-2 x-3 \log (x+1)-\frac{1}{x+1}+\mathrm{c}$, where c is the constant of integration

MHT CET 2025 21st April Morning Shift

MCQ (Single Correct Answer)

-0

If $\quad \int \frac{3 \sin x \cos x}{4 \sin x+7} \mathrm{~d} x=\mathrm{A} \sin x-\mathrm{Blog}(4 \sin x+7)+\mathrm{c}$ where c is the constant of integration, then the value of $\mathrm{A}+\mathrm{B}$ is equal to

$\frac{9}{16}$

$\frac{-9}{16}$

$\frac{33}{16}$

$\frac{-33}{16}$

MHT CET 2025 21st April Morning Shift

MCQ (Single Correct Answer)

-0

$$ \int \frac{\mathrm{d} x}{x\left(x^2+1\right)}= $$

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

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

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

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

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