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1
MHT CET 2021 22th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\int \frac{1}{\cos x+\sqrt{3} \sin x} d x=$$

A
$$2 \log \left[\tan \left(\frac{\mathrm{x}}{2}+\frac{\pi}{12}\right)\right]+\mathrm{c}$$
B
$$\frac{1}{2} \log \left[\tan \left(\frac{\mathrm{x}}{2}-\frac{\pi}{12}\right)\right]+\mathrm{c}$$
C
$$\frac{1}{2} \log \left[\tan \left(\frac{\mathrm{x}}{2}+\frac{\pi}{12}\right)\right]+\mathrm{c}$$
D
$$2 \log \left[\tan \left(\frac{\mathrm{x}}{2}-\frac{\pi}{12}\right)\right]+\mathrm{c}$$
2
MHT CET 2021 22th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

$$\int {{e^x}\left( {{{x - 1} \over {{x^2}}}} \right)dx = } $$

A
$${{ - {e^x}} \over {{x^2}}} + c$$
B
$${{ - {e^x}} \over x} + c$$
C
$${{{e^x}} \over {{x^2}}} + c$$
D
$${{{e^x}} \over x} + c$$
3
MHT CET 2021 22th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

$$\int \sin ^{-1}\left(\frac{2 x}{1+x^2}\right) d x=\quad(\text { where }|x| < 1)$$

A
$$2 \tan ^{-1} x-\log \left|1+x^2\right|+c$$
B
$$x \tan ^{-1} \mathrm{x}+\log \left|1+\mathrm{x}^2\right|+\mathrm{c}$$
C
$$\tan ^{-1} \mathrm{x}+\log \left|1+\mathrm{x}^2\right|+\mathrm{c}$$
D
$$2 x \tan ^{-1} x-\log \left|1+x^2\right|+c$$
4
MHT CET 2021 22th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

$$\int \frac{\sec ^8 x}{\operatorname{cosec} x} d x= $$

A
$$\frac{\sec ^8 x}{8}+c$$
B
$$\frac{\sec ^6 x}{6}+c$$
C
$$\frac{\sec ^7 x}{7}+c$$
D
$$\frac{\sec ^9 x}{9}+c$$
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