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1
TG EAPCET 2024 (Online) 10th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
$ \int \frac{1}{x^{m} \sqrt[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
$\frac{1}{m}\left(\frac{\sqrt[m-1]{x^{m}+1}}{x}\right)^{m}+C$
2
TG EAPCET 2024 (Online) 10th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $\int(\sqrt{\operatorname{cosec} x+1}) d x=k \tan ^{-1}(f(x))+C$, then $\frac{1}{k} f\left(\frac{\pi}{6}\right)=$
A
$\frac{1}{2}$
B
$\frac{1}{4}$
C
$-\frac{1}{4}$
D
$-\frac{1}{2}$
3
TG EAPCET 2024 (Online) 10th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\int \sqrt{4 \cos ^2 x-5 \sin ^2 x} \cos x d x=$
A
$\frac{1}{2} \cos x \sqrt{4-9 \sin ^2 x}+\frac{2}{3} \sin ^{-1}\left(\frac{3 \sin x}{2}\right)+c$
B
$\frac{1}{2} \sin x \sqrt{4-9 \sin ^2 x}+\frac{2}{3} \cos ^{-1}\left(\frac{3 \cos x}{2}\right)+c$
C
$\frac{1}{2} \cos x \sqrt{1-9 \cos ^2 x}+\frac{2}{3} \sin ^{-1}\left(\frac{3 \cos x}{2}\right)+c$
D
$\frac{1}{2} \sin x \sqrt{4-9 \sin ^2 x}+\frac{2}{3} \sin ^{-1}\left(\frac{3 \sin x}{2}\right)+c$
4
TG EAPCET 2024 (Online) 10th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\int\left(\frac{4 \tan ^4 x+3 \tan ^2 x-1}{\tan ^2 x+4}\right) d x=$
A
$4 \tan x-\frac{17}{4} \tan ^{-1}\left(\frac{\tan x}{4}\right)+c$
B
$4 \tan x-\frac{17}{4} \tan ^{-1}\left(\frac{\tan x}{2}\right)+c$
C
$4 \tan x-\frac{17}{2} \tan ^{-1}\left(\frac{\tan x}{2}\right)+c$
D
$2 \tan x-\frac{17}{2} \tan ^{-1}\left(\frac{\tan x}{2}\right)+c$
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