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1
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
$$2 x \tan ^{-1} x-\log \left|1+x^2\right|+c$$
2
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
$$\frac{\sec ^9 x}{9}+c$$
3
MHT CET 2021 21th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\int \frac{1}{x^{\frac{1}{2}}+x^{\frac{1}{3}}} d x=$$

A
$$\sqrt{\mathrm{x}}-\sqrt[3]{\mathrm{x}}+\sqrt[6]{\mathrm{x}}-\log |\sqrt[6]{\mathrm{x}}+1|+c$$
B
$$2 \sqrt{\mathrm{x}}-3 \sqrt[3]{\mathrm{x}}+6 \sqrt[6]{\mathrm{x}}-6 \log |\sqrt[6]{\mathrm{x}}+1|+\mathrm{c}$$
C
$$2 \sqrt{\mathrm{x}}+3 \sqrt[3]{\mathrm{x}}+6 \sqrt[6]{\mathrm{x}}+6 \log |\sqrt[6]{\mathrm{x}}+1|+c$$
D
$$\sqrt{\mathrm{x}}+\sqrt[3]{\mathrm{x}}+\sqrt[6]{\mathrm{x}}+\log |\sqrt[6]{\mathrm{x}}+1|+\mathrm{c}$$
4
MHT CET 2021 21th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\int[\sin |\log x|+\cos |\log x|] d x=$$

A
$$\sin |\log x|+c$$
B
$$x \cos |\log x|+c$$
C
$$\cos |\log x|+c$$
D
$$x \sin |\log x|+c$$
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