1
MHT CET 2021 23rd September Evening Shift
+2
-0

$$\int \frac{d x}{\cos x \sqrt{\cos 2 x}}=$$

A
$$\sin ^{-1}(\tan x)+c$$
B
$$\frac{1}{2} \log \left|\tan \left(\frac{\pi}{4}+x\right)\right|+c$$
C
$$2 \log \left|\frac{1+\tan x}{1-\tan x}\right|+c$$
D
$$\frac{1}{2} \log \left|\frac{1-\tan x}{1+\tan x}\right|+c$$
2
MHT CET 2021 23th September Morning Shift
+2
-0

If $$\int \frac{\sin x}{\sin (x-\alpha)} d x=A x+B \log \sin (x-\alpha)+c$$, then the value of A and B are respectively (where $$\mathrm{c}$$ is a constant of integration)

A
$$\cos \alpha, \sin \alpha$$
B
$$\sin \alpha, \cos \alpha$$
C
$$-\cos \alpha, \sin \alpha$$
D
$$-\sin \alpha, \cos \alpha$$
3
MHT CET 2021 23th September Morning Shift
+2
-0

$$\int \frac{10^{\frac{x}{2}}}{\sqrt{10^{-x}-10^x}} d x=$$

A
$$2 \sqrt{10^{-x}+10^x}+c$$
B
$$\frac{2}{2 \sqrt{10^{-x}+10^x}}+c$$
C
$$\frac{1}{\log 10} \sin ^{-1}\left(10^{\mathrm{x}}\right)+\mathrm{c}$$
D
$$\frac{1}{\log 10} \cos ^{-1}\left(10^x\right)+c$$
4
MHT CET 2021 23th September Morning Shift
+2
-0

$$\int e^{\left(e^x+x\right)} d x=$$

A
$$e^x+x+c$$
B
$$e^{\left(e^x\right)} \cdot x+c$$
C
$$e^{\left(e^x\right)}+c$$
D
$$e^{\left(e^x\right)}\left(e^x-1\right)+c$$
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