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

If $$\int \frac{1+x^2}{1+x^4} d x=\frac{1}{\sqrt{2}} \tan ^{-1}\left[\frac{f(x)}{\sqrt{2}}\right]+c$$, then $$f(x)=$$

A
$$x+\frac{1}{x^2}$$
B
$$x-\frac{1}{x^2}$$
C
$$x+\frac{2}{x}$$
D
$$x-\frac{1}{x}$$
2
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
$$\log (1+\cos x)+c$$
3
MHT CET 2020 16th October Evening Shift
+2
-0

$$\int\left[-\frac{\log x-1}{1+(\log x)^2}\right]^2 d x=$$

A
$$\frac{x}{1+(\log x)^2}+c$$
B
$$\frac{x}{(1+\log x)}+c$$
C
$$\frac{x^2}{1+(\log x)^2}+c$$
D
$$\frac{1}{1+(\log x)^2}+c$$
4
MHT CET 2020 16th October Evening Shift
+2
-0

$$\int \frac{d x}{\cos 2 x-\cos ^2 x}=$$

A
$$-\tan x+c$$
B
$$\cot x+c$$
C
$$\tan x+c$$
D
$$-\cot x+c$$
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