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

If $$\int {{{5\tan x} \over {\tan x - 2}}dx = x + a\log |\sin x - 2\cos x| + c}$$, then a = (Where c is constant of integration)

A
1
B
$$-$$2
C
$$-$$1
D
2
2
MHT CET 2021 21th September Morning Shift
+2
-0

$$\int[1+2 \tan x(\tan x+\sec x)]^{\frac{1}{2}} d x=$$

A
$$\log [\sec x(\sec x-\tan x)]+c$$
B
$$\log [\operatorname{cosec} x(\sec x+\tan x)]+c$$
C
$$\log [\sec x(\sec x+\tan x)]+c$$
D
$$\log [\sec \mathrm{x}+\tan \mathrm{x}]+\mathrm{c}$$
3
MHT CET 2021 21th September Morning Shift
+2
-0

If $$\int \frac{x^3}{\sqrt{1+x^2}} d x=a\left(1+x^2\right)^{\frac{3}{2}}+b \sqrt{1+x^2}+c$$, then $$a+b=$$, (where $$c$$ is constant of integration)

A
$$\frac{-2}{3}$$
B
$$\frac{-1}{3}$$
C
$$\frac{1}{3}$$
D
$$\frac{2}{3}$$
4
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
$$\mathrm{e}^{\tan x}+\tan \mathrm{x}+\mathrm{c}$$
MHT CET Subjects
Physics
Mechanics
Optics
Electromagnetism
Modern Physics
Chemistry
Physical Chemistry
Inorganic Chemistry
Organic Chemistry
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Algebra
Trigonometry
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