1
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

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

2
TS EAMCET 2023 (Online) 13th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

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

A

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

B

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

C

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

D

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

3
TS EAMCET 2023 (Online) 13th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $\frac{3 \pi}{2} < x < \frac{5 \pi}{2}$ and $\int(\sqrt{1-\sin x}+\sqrt{1+\sin x}) d x=f(x)+C$, where $C$ is the constant of integration, then $f\left(\frac{\pi}{3}\right)-f(0)=$

A

2

B

-2

C

$2 \sqrt{2}$

D

$-2 \sqrt{2}$

4
TS EAMCET 2023 (Online) 13th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

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 $f\left(\frac{\pi}{2}\right)-f(0)=$

A

$2 \log 2$

B

0

C

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

D

1

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