1
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
$$e^{\left(e^x\right)}\left(e^x-1\right)+c$$
2
MHT CET 2021 22th September Evening Shift
+2
-0

$$\int \frac{\tan ^4 \sqrt{x} \cdot \sec ^2 \sqrt{x}}{\sqrt{x}} d x=$$

A
$$\frac{-5}{2}[\tan \sqrt{x}]^5+c$$
B
$$[\tan \sqrt{\mathrm{x}}]^5+c$$
C
$$\frac{2}{5}[\tan \sqrt{x}]^5+c$$
D
$$\frac{5}{2}[\tan \sqrt{x}]^5+c$$
3
MHT CET 2021 22th September Evening Shift
+2
-0

$$\int \cos ^{-1} x d x=$$

A
$$x \cos ^{-1} x+\sqrt{1-x^2}+c$$
B
$$-x \cos ^{-1} x+\sqrt{1+x^2}+c$$
C
$$x \cos ^{-1} x-\sqrt{1+x^2}+c$$
D
$$x \cos ^{-1} x-\sqrt{1-x^2}+c$$
4
MHT CET 2021 22th September Evening Shift
+2
-0

$$\int \frac{1}{\cos x+\sqrt{3} \sin x} d x=$$

A
$$2 \log \left[\tan \left(\frac{\mathrm{x}}{2}+\frac{\pi}{12}\right)\right]+\mathrm{c}$$
B
$$\frac{1}{2} \log \left[\tan \left(\frac{\mathrm{x}}{2}-\frac{\pi}{12}\right)\right]+\mathrm{c}$$
C
$$\frac{1}{2} \log \left[\tan \left(\frac{\mathrm{x}}{2}+\frac{\pi}{12}\right)\right]+\mathrm{c}$$
D
$$2 \log \left[\tan \left(\frac{\mathrm{x}}{2}-\frac{\pi}{12}\right)\right]+\mathrm{c}$$
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