TS EAMCET 2023 (Online) 13th May Evening Shift | Indefinite Integration Question 62 | Mathematics

If $\int \frac{2 \sin 2 x-3 \cos x}{2 \sin ^2 x-3 \sin x+4} d x=f(x)+C$, where $C$ is the constant of integration, then $f\left(\frac{\pi}{2}\right)-f(0)=$

$2 \log 2$

$\log \left(\frac{3}{4}\right)$

TS EAMCET 2023 (Online) 13th May Evening Shift

MCQ (Single Correct Answer)

-0

$\int \frac{2 x+3}{\sqrt{3 x^2-2 x+1}} d x=$

$\frac{2}{3} \sqrt{3 x^2-2 x+1}+\frac{11}{3} \sinh ^{-1}\left(\frac{3 x-1}{\sqrt{2}}\right)+C$

$\frac{1}{3} \sqrt{3 x^2-2 x+1}+\frac{11}{3} \sinh ^{-1}\left(\frac{\sqrt{3} x-1}{\sqrt{2}}\right)+C$

$\frac{1}{3} \sqrt{3 x^2-2 x+1}+\frac{11}{3} \sinh ^{-1}\left(\frac{3 x-1}{\sqrt{3}}\right)+C$

$\frac{2}{3} \sqrt{3 x^2-2 x+1}+\frac{11}{3 \sqrt{3}} \sinh ^{-1}\left(\frac{3 x-1}{\sqrt{2}}\right)+C$

TS EAMCET 2023 (Online) 13th May Morning Shift

MCQ (Single Correct Answer)

-0

$$ \int \frac{1}{16-7 \sin ^2 x} d x= $$

$\frac{1}{12} \tan ^{-1}\left(\frac{3 \tan x}{4}\right)+C$

$\frac{1}{3} \sin ^{-1}\left(\frac{3 \sin x}{4}\right)+C$

$\frac{1}{12} \log \left(\frac{4-\sqrt{7} \sin x}{4+\sqrt{7} \sin x}\right)+C$

$\frac{1}{12} \log \left(\frac{4+\sqrt{7} \sin x}{4-\sqrt{7} \sin x}\right)+C$

TS EAMCET 2023 (Online) 13th May Morning Shift

MCQ (Single Correct Answer)

-0

$$ \int \frac{\sec ^2 x}{(\sec x+\tan x)^2} d x= $$

$\frac{3+(\sec x+\tan x)^2}{2(\sec x+\tan x)^3}+C$

$-\frac{1+3(\sec x+\tan x)^2}{6(\sec x+\tan x)^3}+C$

$-\frac{3+(\sec x+\tan x)^2}{2(\sec x+\tan x)^3}+C$

$-\frac{1+(\sec x+\tan x)}{3(\sec x+\tan x)^2}+C$

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