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

$$\int \frac{2 x^2-1}{x^4-x^2-20} d x=$$

A
$$\frac{1}{\sqrt{5}} \log \left|\frac{x+\sqrt{5}}{x-\sqrt{5}}\right|+\tan ^{-1}\left(\frac{x}{2}\right)+c$$
B
$$\frac{1}{2 \sqrt{5}} \log \left|\frac{x+\sqrt{5}}{x-\sqrt{5}}\right|+\tan ^{-1}\left(\frac{x}{2}\right)+c$$
C
$$\frac{1}{2 \sqrt{5}} \log \left|\frac{x-\sqrt{5}}{x+\sqrt{5}}\right|+\frac{1}{2} \tan ^{-1}\left(\frac{x}{2}\right)+c$$
D
$$\frac{1}{2} \log \left|\frac{x-\sqrt{5}}{x+\sqrt{5}}\right|+\frac{1}{2} \tan ^{-1}\left(\frac{x}{2}\right)+c$$
2
MHT CET 2021 20th September Morning Shift
+2
-0

$$\int \tan ^{-1}(\sec x+\tan x) d x=$$

A
$$\frac{\pi x}{4}+\frac{x^2}{4}+c$$
B
$$\sin x \cos x+c$$
C
$$\frac{\pi x}{2}+\frac{x^2}{2}+c$$
D
$$\sin x+\cos x+c$$
3
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
$$x-\frac{1}{x}$$
4
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
$$\log (1+\cos x)+c$$
MHT CET Subjects
Physics
Mechanics
Optics
Electromagnetism
Modern Physics
Chemistry
Physical Chemistry
Inorganic Chemistry
Organic Chemistry
Mathematics
Algebra
Trigonometry
Calculus
Coordinate Geometry
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