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Question

2sin5xsin3xdx=

A
sin2x4sin8x16+c
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B
18[4sin2xsin8x]+c
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C
116[4cos2xcos8x]+c
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D
116[4cos2x+cos8x]+c
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Solution

The correct option is B 18[4sin2xsin8x]+c
Let I=2sin5xsin3xdx
We know that,
2sinAsinB=cos(ab)cos(a+b)
So,
2sin5x.sin3x=cos(2x)cos(8x)
Then,
I=[cos(2x)cos(8x)]dx
=(cos2x).dx
cos2xdx =sin2x2
cos8xdx =sin8x8
I=sin2x2sin8x8+c
=18[4sin2xsin8x]+c
Hence, 2sin5xsin3x=18[4sin2xsin8x]+c

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