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1
COMEDK 2023 Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$\int x^x(1+\log x) d x$$ is equal to

A
$$ x \log x+c $$
B
$$ x^x+c $$
C
$$ x^x \log x+c $$
D
$$ x^{x-1}+c $$
2
COMEDK 2023 Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int \sqrt{\operatorname{cosec} x-1} d x= $$

A
$$ \log \left|\sin x+\sqrt{\sin ^2 x+\sin x}\right|+c $$
B
$$ \log \left|\sin x+1+2 \sqrt{\sin ^2 x+\sin x}\right|+c $$
C
$$ \log \left|\sin x+\frac{1}{2}+\sqrt{\sin ^2 x+\sin x}\right|+c $$
D
$$ \log \left|\sin x+\frac{1}{2}+\sqrt{\sin ^2 x+\frac{1}{2}+\sin x}\right|+c $$
3
COMEDK 2023 Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int e^x\left(1+\tan x+\tan ^2 x\right) d x \text { is equal to } $$

A
$$ e^x \cos x+c $$
B
$$ e^x \sin x+c $$
C
$$ e^x \tan x+c $$
D
$$ e^x \sec x+c $$
4
COMEDK 2023 Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int \frac{\cos 4 x+1}{\cot x-\tan x} d x= $$

A
$$ -\frac{1}{2} \cos 2 x+c $$
B
$$ -\frac{1}{8} \cos 4 x+c $$
C
$$ -\frac{1}{4} \cos 4 x+c $$
D
$$ -\frac{1}{16} \cos 8 x+c $$
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