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Question

sinx.cosx.cos2x.cos4x.cos8x.cos16xdx is equal to

A
sin16x1024+c
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B
cos32x1024+c
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C
cos32x1096+c
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D
none
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Solution

The correct option is D cos32x1024+c
sinx.cosx.cos2x.cos4x.cos8x.cos16xdx

12(2sinx.cosx)cos2x.cos4x.cos8x.cos16xdx

122(2sin2x.cos2x)cos4x.cos8x.cos16xdx

123(2sin4x.cos4x).cos8x.cos16xdx

124(2sin8x.cos8x).cos16xdx

125(2sin16xcos16x)dx

132sin32xdx

132×(cos32x)32+c

cos32x1024+c

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