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1
TS EAMCET 2023 (Online) 14th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $\int \frac{x^{49} \tan ^{-1}\left(x^{50}\right)}{\left(1+x^{100}\right)} d x=k\left(\tan ^{-1}\left(x^{50}\right)\right)^2+C$, then $k=$

A

$\frac{-1}{100}$

B

$\frac{1}{50}$

C

$\frac{-1}{50}$

D

$\frac{1}{100}$

2
TS EAMCET 2023 (Online) 14th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

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 $A-(B+C+D)=$

A

172

B

184

C

192

D

216

3
TS EAMCET 2023 (Online) 14th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

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

A

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

B

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

C

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

D

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

4
TS EAMCET 2023 (Online) 14th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

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

A

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

B

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

C

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

D

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

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