1
MHT CET 2021 24th September Evening Shift
+2
-0

$$\int e^x\left(\frac{1+\sin x}{1+\cos x}\right) d x=$$

A
$$e^x \tan \frac{x}{2}+c$$
B
$$e^x \cot \frac{x}{2}+c$$
C
$$e^x \cos \frac{x}{2}+c$$
D
$$e^x \sin \frac{x}{2}+c$$
2
MHT CET 2021 24th September Evening Shift
+2
-0

$$\int \cos ^3 x e^{\log (\sin x)^2} d x=$$

A
$$\frac{\sin ^3 x}{3}-\sin ^5 x+c$$
B
$$\frac{\sin ^3 x}{3}-\frac{\sin ^5 x}{5}+c$$
C
$$\frac{\sin ^3 x}{3}+\frac{\sin ^5 x}{5}+c$$
D
$$\sin ^3 x+\sin ^5 x+c$$
3
MHT CET 2021 24th September Evening Shift
+2
-0

$$\int \frac{d x}{e^x+e^{-x}+2}=$$

A
$$\frac{1}{\mathrm{e}^{2 \mathrm{x}}+1}+\mathrm{c}$$
B
$$\frac{-1}{\mathrm{e}^{\mathrm{x}}+1}+\mathrm{c}$$
C
$$\frac{1}{e^x}+c$$
D
$$\frac{-1}{e^x}+c$$
4
MHT CET 2021 24th September Morning Shift
+2
-0

$$\int \frac{\mathrm{dx}}{32-2 \mathrm{x}^2}=\mathrm{A} \log (4-\mathrm{x})+\mathrm{B} \log (4+\mathrm{x})+\mathrm{c}$$, then the values of $$\mathrm{A}$$ and $$\mathrm{B}$$ are respectively (where c is a constant of integration)

A
$$\frac{-1}{8}, \frac{1}{8}$$
B
$$\frac{1}{8}, \frac{-1}{8}$$
C
$$\frac{-1}{16}, \frac{1}{16}$$
D
$$\frac{1}{8}, \frac{1}{8}$$
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