1
MHT CET 2021 21th September Morning Shift
+2
-0

$$\int e^{\tan x}\left(\sec ^2 x+\sec ^3 x \sin x\right) d x=$$

A
$$\tan x \cdot e^{\tan x}+c$$
B
$$(1+\tan \mathrm{x}) \mathrm{e}^{\tan \mathrm{x}}+\mathrm{c}$$
C
$$\sec \mathrm{x} \cdot \mathrm{e}^{\tan \mathrm{x}}+\mathrm{c}$$
D
$$\mathrm{e}^{\tan x}+\tan \mathrm{x}+\mathrm{c}$$
2
MHT CET 2021 20th September Evening Shift
+2
-0

$$\int \sec ^4 x \cdot \tan ^4 x d x=\frac{\tan ^m x}{m}+\frac{\tan ^n x}{n}+c$$ (where c is constant of integration), then m + n =

A
8
B
12
C
10
D
16
3
MHT CET 2021 20th September Evening Shift
+2
-0

$$\int \operatorname{cosec}(x-a) \operatorname{cosec} x d x=$$

A
$$\operatorname{cosec} a \cdot \log [\sin (x-a) \operatorname{cosec} x]+c$$
B
$$\operatorname{cosec} a \log [\sin (x-a) \sin x]+c$$
C
$$\sin a \cdot \log [\sin (x-a) \sin x]+c$$
D
$$\operatorname{cosec} a \cdot \log [\operatorname{cosec}(x-a) \sin x]+c$$
4
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
$$\frac{1}{2} \log \left|\frac{x-\sqrt{5}}{x+\sqrt{5}}\right|+\frac{1}{2} \tan ^{-1}\left(\frac{x}{2}\right)+c$$
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