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Q.

cos8xcos7x1+2cos5xdx is equal to 

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a

13sin3x+12sin2x+c

b

13sin3x12sin2x+c

c

115sin3x+110sin2x+c

d

23sin3x22sin2x+c

answer is D.

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Detailed Solution

  cos8xcos7x1+2cos5x dx =-2 sin15x2 sinx21+2 cos 5xdx =(-2)3 sin5x2-4 sin35x21+2(1-2 sin25x2) =(-2)3-4 sin25x2sin5x2 sinx23-4 sin25x2 =cos 3x-cos 2xdx =sin 3x3-sin 2x2+c   

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∫cos8x−cos7x1+2cos5x dx is equal to