1
MHT CET 2022 11th August Evening Shift
+2
-0

$$\int \frac{\sin \frac{5 x}{2}}{\sin \frac{x}{2}} d x=$$

(where $$C$$ is a constant of integration.)

A
$$x+\sin x+\sin 2 x+C$$
B
$$x+\sin x+\sin 2 x-C$$
C
$$x+2 \sin x+2 \sin 2 x+C$$
D
None of these
2
MHT CET 2022 11th August Evening Shift
+2
-0

$$\text { If } \int e^{x^2} \cdot x^3 \mathrm{~d} x=e^{x^2} \cdot[f(x)+C]$$ (where $$C$$ is a constant of integration.) and $$f(1)=0$$, then value of $$f(2)$$ will be

A
$$\frac{-3}{2}$$
B
$$\frac{-1}{2}$$
C
$$\frac{3}{2}$$
D
$$\frac{1}{2}$$
3
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
$$e^x \sin \frac{x}{2}+c$$
4
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
$$\sin ^3 x+\sin ^5 x+c$$
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