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1
COMEDK 2026 Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int \frac{e^{\log \left(1+\frac{1}{x^2}\right)}}{x^2+\frac{1}{x^2}} d x= $$

A

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

B

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

C

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

D

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

2
COMEDK 2025 Evening Shift
MCQ (Single Correct Answer)
+1
-0
$$\int \frac{\sin 2 x}{(1+\sin x)(2+\sin x)} d x=a \log |1+\sin x|-b \log |2+\sin x|+c$$ then the value of $a$ and $b$ is ----------------
A
$a=-2, b=4$
B
$a=2, b=4$
C
$a=-2, b=-4$
D
$a=2, b=-4$
3
COMEDK 2025 Evening Shift
MCQ (Single Correct Answer)
+1
-0
$\int\left(e^{x \log _e 6}\right) e^x d x=\phi(x)+c$ then $\phi(x)=$
A
$6^x e^x$
B
$\frac{e^x}{\log 6 e}$
C
$\frac{6^x}{1+\log _e 6}$
D
$\frac{(6 e)^x}{1+\log _e 6}$
4
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
$\log \sin (\cos x)$
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