A) \[2x+sinx+2sin2x+c\]
B) \[x+2sinx+2sin2x+c\]
C) \[x+2sinx+sin2x+c\]
D) \[2x+sinx+sin2x+c\]
Correct Answer: C
Solution :
\[\int_{{}}^{{}}{\frac{\sin \frac{5x}{2}}{\sin \frac{x}{2}}}dx=\int_{{}}^{{}}{\frac{2\sin \frac{5x}{2}\cos \frac{x}{2}}{2\sin \frac{x}{2}\cos \frac{x}{2}}}dx\] \[=\int_{{}}^{{}}{\frac{\sin 3x+\sin 2x}{\operatorname{sinx}}}dx\] \[=\int_{{}}^{{}}{\frac{3\sin x-4{{\sin }^{3}}x-2\sin x\cos x}{\sin \,x}}dx\] \[=\int_{{}}^{{}}{(3-4{{\sin }^{2}}x+2cos\,x)\,}dx\] \[=\int_{{}}^{{}}{(3-2(1-cos2\,x)+2cos\,}x)dx\] \[=\int_{{}}^{{}}{(1+2cos2\,x+2cos\,}x)dx\] \[=x+\sin 2x+2\sin x+c\]
You need to login to perform this action.
You will be redirected in
3 sec
