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1
COMEDK 2025 Afternoon Shift
MCQ (Single Correct Answer)
+1
-0
$\int \frac{\sin x+\cos x}{\sqrt{1+2 \sin x \cos x}} d x=\varphi(x)+C$ Then $\varphi(x)=$
A
$\log x$
B
$x$
C
$\log (\sin x+\cos x)$
D
$\log \sin (\cos x)$
2
COMEDK 2025 Afternoon Shift
MCQ (Single Correct Answer)
+1
-0
$\int \frac{e^{\tan ^{-1} x}}{\left(1+x^2\right)}\left(1+x+x^2\right) d x=$
A
$e^{\tan ^{-1} x}+c$
B
$x e^{\tan ^{-1} x}+c$
C
$\frac{e^{\tan ^{-1} x}}{\left(1+x^2\right)}+c$
D
$\frac{x e^{\tan ^{-1} x}}{\left(1+x^2\right)}+c$
3
COMEDK 2025 Afternoon Shift
MCQ (Single Correct Answer)
+1
-0
$\int \frac{x}{(x-1)(x-2)^2} d x=a \log \left|\frac{x-1}{x-2}\right|+\frac{b}{(x-2)}+c$ then
A
$a=-1, b=2$
B
$a=-1, b=-2$
C
$a=1, b=-2$
D
$a=1, b=2$
4
COMEDK 2025 Afternoon Shift
MCQ (Single Correct Answer)
+1
-0
$\int \frac{d x}{x \sqrt{4 x^2-9}}=$
A
$\frac{2}{3} \log \left|\frac{x-3}{x+3}\right|+c$
B
$\frac{4}{3} \tan ^{-1}\left(\frac{\sqrt{4 x^2-9}}{3}\right)+c$
C
$\frac{2}{3} \log \left|\frac{x+3}{x-3}\right|+c$
D
$\frac{1}{3} \tan ^{-1}\left(\frac{\sqrt{4 x^2-9}}{3}\right)+c$
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