∫(2x-1)cos(2x-1)2+54x2-4x+6dx is equal to

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12sin(2x−1)2+5+c

12cos(2x+1)2+5+c

12cos(2x−1)2+5+c

12sin(2x+1)2+5+c

answer is A.

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Detailed Solution

The given integral becomes ∫(2x−1)cos(2x−1)2+52x−12+5dxSubstitute 2x−12+5=t2, and 22x−1.2dx=2t dt∫costt.12t dt=12∫costdt=12sint=12sin2x−12+5+C

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