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1
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $$\int \frac{1}{\sqrt{\sin ^3 x \cos x}} d x=\frac{k}{\sqrt{\tan x}}+c$$ then the value of $$k$$ is

A
$$-2$$
B
1
C
2
D
$$-1$$
2
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$\int \sqrt{x^2-4 x+2} d x=$$

A
$$ \frac{1}{2}(x-2) \sqrt{x^2-4 x+2}+\log \left|(x-2)+\sqrt{x^2-4 x+2}\right|+C $$
B
$$ (x-2) \sqrt{x^2-4 x+2}+\frac{1}{2} \log \left|(x-2)+\sqrt{x^2-4 x+2}\right|+C $$
C
$$ \frac{1}{2}(x-2) \sqrt{x^2-4 x+2}-\sin ^{-1} \frac{x-2}{\sqrt{2}}+C $$
D
$$ \frac{1}{2}(x-2) \sqrt{x^2-4 x+2}-\log \left|(x-2)+\sqrt{x^2-4 x+2}\right|+C $$
3
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int \frac{x}{x^4-16} d x= $$

A
$$ \frac{1}{16} \log \left|\frac{x^2+4}{x^2-4}\right|+C $$
B
$$ \frac{1}{4} \log \left|\frac{x^2+4}{x^2-4}\right|+C $$
C
$$ \frac{1}{16} \log \left|\frac{x^2-4}{x^2+4}\right|+C $$
D
$$ \frac{1}{8} \log \left|\frac{x^2-4}{x^2+4}\right|+C $$
4
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { The value of } \int \frac{1}{x+\sqrt{x-1}} d x \text { is } $$

A
$$ \log (x+\sqrt{x-1})+\sin ^{-1}\left(\sqrt{\frac{x-1}{x}}\right)+C $$
B
$$ \log (x+\sqrt{x-1})-\frac{2}{\sqrt{3}} \tan ^{-1}\left(\frac{2 \sqrt{x-1}+1}{\sqrt{3}}\right)+C $$
C
$$ \log (x+\sqrt{x-1})+C $$
D
$$ \log (x-1+\sqrt{x-1})+\frac{1}{\sqrt{3}} \log \left|\frac{x-2-\sqrt{3}}{x-2+\sqrt{3}}\right|+C $$
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