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

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

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

If $$\int \frac{(\cos x-\sin x)}{8-\sin 2 x} d x=\frac{1}{p} \log \left[\frac{3+\sin x+\cos x}{3-\sin x-\cos x}\right]+c$$, then $$p=$$ (where $$\mathrm{c}$$ is a constant of integration)

A
12
B
$$\frac{1}{6}$$
C
6
D
3
3
MHT CET 2021 23rd September Evening Shift
+2
-0

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

A
$$x \sec ^{-1} x+\log \left|x+\sqrt{x^2-1}\right|+c$$
B
$$x \sec ^{-1} x-\log \left|x+\sqrt{x^2-1}\right|+c$$
C
$$x \sec ^{-1} x-\log \left|x+\sqrt{x^2+1}\right|+c$$
D
$$x \sec ^{-1} x+\log \left|x+\sqrt{x^2+1}\right|+c$$
4
MHT CET 2021 23rd September Evening Shift
+2
-0

If $$\int \frac{\sqrt{x}}{x(x+1)} d x=k \tan ^{-1} m+c$$, (where c is constant of integration), then

A
$$k=1, m=\sqrt{x}$$
B
$$k=2, m=\sqrt{x}$$
C
$$\mathrm{k}=1, \mathrm{~m}=\mathrm{x}$$
D
$$\mathrm{k}=2, \mathrm{~m}=\mathrm{x}$$
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