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Question

sin3xcos4xcosxdx is equal to

A
14log|cos4X|log|cosx|+c
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B
14log|cos4x|+log|cosx|+c
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C
14log|sin4x|+log|cos4x|+c
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D
14log|sin4x|log|cos4x|+c
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Solution

The correct option is A 14log|cos4x|+log|cosx|+c
sin3xcos4xcosxdx

=sin(4xx)cos 4xcos xdx

=[sin(4x)cos xcos(4x)sin x](cos 4x)(cos x)dx

=tan 4x dxtan x dx

=14log|sec 4x|log|sec x|+c

=14log|cos 4x|+log|cos x|+c

sin 3xcos 4x cos xdx=14log|cos 4x|+log|cos x|+c

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