1
MHT CET 2021 20th September Morning Shift
+2
-0

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

A
$$x \tan \left(\frac{x}{2}\right)+c$$
B
$$\log (x+\sin x)+c$$
C
$$\cot \left(\frac{x}{2}\right)+c$$
D
$$\log (1+\cos x)+c$$
2
MHT CET 2020 16th October Morning Shift
+2
-0

If $$\int \frac{\sin \theta}{\sin 3 \theta} d \theta=\frac{1}{2 k} \log \left|\frac{k+\tan \theta}{k-\tan \theta}\right|+c$$, then $$k=$$

A
$$\sqrt{7}$$
B
$$\sqrt{5}$$
C
$$\sqrt{2}$$
D
$$\sqrt{3}$$
3
MHT CET 2020 16th October Morning Shift
+2
-0

If $$\int \sqrt{x-\frac{1}{x}}\left(\frac{x^2+1}{x^2}\right) d x=\frac{2}{3}\left(x-\frac{1}{x}\right)^k+c$$, then value of $$k$$ is

A
$$\frac{2}{3}$$
B
$$\frac{3}{2}$$
C
$$\frac{5}{2}$$
D
$$\frac{2}{5}$$
4
MHT CET 2020 16th October Morning Shift
+2
-0

$$\int \cot x \cdot \log [\log (\sin x)] d x=$$

A
$$\log (\sin x)[\log (\log (\sin x))-1]+c$$
B
$$\log (\sin x)[\log (\log (\sin x))+1]+c$$
C
$$\log (\sin x)[\log (\sin x))+1]+c$$
D
$$\log (\sin x)[\log (\sin x)-1]+c$$
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