TS EAMCET 2023 (Online) 14th May Morning Shift | Indefinite Integration Question 57 | Mathematics

If $\int(\log x)^3 x^5 d x=\frac{x^6}{A}\left[B(\log x)^3\right. \left.+C(\log x)^2+D(\log x)-1\right]+k$ and $A, B, C, D$ are integers, then $A-(B+C+D)=$

172

184

192

216

TS EAMCET 2023 (Online) 14th May Morning Shift

MCQ (Single Correct Answer)

-0

$$ \int \frac{d x}{\left(x^2+1\right)\left(x^2+4\right)}= $$

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

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

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

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

TS EAMCET 2023 (Online) 14th May Morning Shift

MCQ (Single Correct Answer)

-0

$\int \frac{d x}{(x-1)^{\frac{3}{4}}(x+2)^{\frac{5}{4}}}=$

$\frac{4}{3}\left(\frac{x-1}{x+2}\right)^{1 / 4}+C$

$\frac{3}{4}\left(\frac{x-1}{x-2}\right)^{1 / 4}+C$

$\frac{4}{3}\left(\frac{x+2}{x-1}\right)^{1 / 4}+C$

$\frac{3}{4}\left(\frac{x-2}{x-1}\right)^{1 / 4}+C$

TS EAMCET 2023 (Online) 13th May Evening Shift

MCQ (Single Correct Answer)

-0

$\int \frac{1}{\left(x+\frac{2}{x}\right) \sqrt{x^4+4 x^2+3}} d x=$

$\frac{1}{2} \sec ^{-1}\left(x^2+2\right)+C$

$-\operatorname{cosech}^{-1}\left(x^2+2\right)+C$

$\frac{1}{2} \tan ^{-1}\left(x+\frac{2}{x}\right)+C$

$-\frac{1}{2} \cot ^{-1}\left(x+\frac{2}{x}\right)+C$

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