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1
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
$$ e^x \sec x+c $$
2
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
$$ -\frac{1}{16} \cos 8 x+c $$
3
COMEDK 2022
MCQ (Single Correct Answer)
+1
-0

$$\int \frac{1}{x \sqrt{a x-x^2}} d x$$ is

A
$$\frac{-3}{a} \sqrt{\frac{a-x}{x}}+C$$
B
$$-\frac{2}{a} \sqrt{\frac{x}{a-x}+C}$$
C
$$\frac{-2}{a} \sqrt{\frac{a-x}{x}}+C$$
D
None of these
4
COMEDK 2022
MCQ (Single Correct Answer)
+1
-0

$$\int \frac{3^x}{\sqrt{1-9^x}} d x$$ is equal to

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