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1
TG EAPCET 2024 (Online) 9th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\int \frac{\left(1-4 \sin ^2 x\right) \cos x}{\cos (3 x+2)} d x=$
A
$\frac{1}{2 \sqrt{2}} \tan ^{-1}\left(\frac{x^4-1}{\sqrt{2} x^2}\right)+c$
B
$\log \left(x^5+x^2\right)-\log \left(x^3+x\right)+\log (x+1)+c$
C
$\frac{2}{9} x^8-\frac{4}{9} x^6+\frac{1}{9} x^4-\frac{1}{3} x^2+c$
D
$\frac{1}{\sqrt{2}} \tan ^{-1}\left(\frac{x^5-1}{\sqrt{2} x^3}\right)+c$
2
TG EAPCET 2024 (Online) 9th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\int \frac{1}{x^{m \sqrt[m]{m}} x^{m}+1} d x=$
A
$\frac{1}{m-1}\left(\frac{\sqrt[m]{x^{m}+1}}{x}\right)^{m}+C$
B
$\frac{-1}{m-1}\left(\frac{\sqrt[m]{x^{m}+1}}{x}\right)^{m-1}+C$
C
$\frac{-1}{m}\left(\frac{\sqrt[m]{x^{m}+1}}{x}\right)^{m}+C$
D
$\frac{1}{m}\left(\frac{\sqrt[m-1]{x^{m}+1}}{x}\right)^{m}+C$
3
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

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

4
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

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

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