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1
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\int \frac{1}{\sqrt{9+8 x-x^2}} d x=\varphi(x)+c$ then $\varphi(x)=$
A
$\frac{1}{5} \sin ^{-1}\left(\frac{x-4}{5}\right)$
B
$\sin ^{-1}\left(\frac{x-4}{5}\right)$
C
$\frac{1}{10} \log \left|\frac{4-x}{4+x}\right|$
D
$\log \left|\frac{4-x}{4+x}\right|$
2
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\int \tan ^2\left(5-\frac{x}{2}\right) d x=$
A
$-\frac{1}{2} \tan \left(5-\frac{x}{2}\right)-x+c$
B
$-2 \tan \left(5-\frac{x}{2}\right)+c$
C
$\tan \left(5-\frac{x}{2}\right)+c$
D
$-2 \tan \left(5-\frac{x}{2}\right)-x+c$
3
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\int \log x^2 d x=$
A
$\log x^2+x+c$
B
$x \log x^2-1+c$
C
$x \log x^2+x+c$
D
$x \log x^2-2 x+c$
4
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\int \frac{d x}{(x+2)\left(x^2+1\right)}=p \log |x+2|+q \log \left|x^2+1\right|+r \tan ^{-1} x+c$ then $p+q+r=$
A
$\frac{2}{5}$
B
$\frac{1}{2}$
C
$\frac{7}{10}$
D
16
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