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

$$ \int \frac{\tan x}{\sec ^2 x\left(1+\sec ^6 x\right)^{\frac{2}{3}}} d x= $$

A

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

B

$2\left(1+\sec ^6 x\right)^{\frac{4}{3}}+C$

C

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

D

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

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

$$ \int \frac{1}{(x-1)^{\frac{5}{7}}(x+1)^{\frac{9}{7}}} d x= $$

A

$\frac{7}{4}\left(\frac{x+1}{x-1}\right)^{\frac{2}{7}}+C$

B

$\frac{-7}{4}\left(\frac{x+1}{x-1}\right)^{\frac{2}{7}}+C$

C

$\frac{7}{4}\left(\frac{x-1}{x+1}\right)^{\frac{2}{7}}+C$

D

$\frac{-7}{4}\left(\frac{x-1}{x+1}\right)^{\frac{2}{7}}+C$

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

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

A

$-\frac{x}{2}+\frac{\sqrt{3}}{2} \log \left|\sin \left(x-\frac{\pi}{3}\right)\right|+C$

B

$\frac{x}{2}+\frac{\sqrt{3}}{2} \log \left|\sin \left(x-\frac{\pi}{3}\right)\right|+C$

C

$-\frac{x}{2}-\frac{\sqrt{3}}{2} \log \left[\sin \left(x-\frac{\pi}{3}\right)\right]+C$

D

$\frac{x}{2}-\frac{\sqrt{3}}{2} \log \left|\sin \left(x-\frac{\pi}{3}\right)\right|+C$

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

$$ \begin{aligned} & \text { If } \int \frac{1}{\operatorname{cosec} x+\cos x} d x=\frac{1}{2 \sqrt{3}} \log |f(x)| \\ & -\int \frac{\cos x-\sin x}{2+\sin 2 x} d x+c, \text { then at } x=\frac{\pi}{3},|f(x)|= \end{aligned} $$

A

$\frac{3 \sqrt{3}-1}{\sqrt{3}+1}$

B

$\frac{3 \sqrt{3}+1}{\sqrt{3}+1}$

C

$\frac{6 \sqrt{3}-2}{\sqrt{3}+1}$

D

$\frac{6 \sqrt{3}+2}{\sqrt{3}+1}$

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