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Q.

If ∫(2x−1)dxx4−2x3+x+1=Atan−1⁡f(x)3+C then

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a

A=13

b

A=2

c

f(x)=2x2−2x−1

d

f(x)=2x2+2x+1

answer is C.

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Detailed Solution

I=∫(2x−1)dxx2−x2−x2−x+1 Put x2−x=tI=∫dtt2−t+1=∫dtt−122+34I=∫dtt−122+322⇒I=23tan−1⁡2x2−2x−13+C
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If ∫(2x−1)dxx4−2x3+x+1=Atan−1⁡f(x)3+C then