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Q.

If f(x)=x2−a2 then ∫x2f(x)dx is

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a

xf(x)+a22log⁡|x+f(x)|+C

b

x22f(x)−a22log⁡|x+f(x)|+C

c

x22f(x)+a2log⁡|x−f(x)|+C

d

x2f(x)+a22log⁡|x+f(x)|+C

answer is D.

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Detailed Solution

I=∫x2x2−a2dx=∫x2−a2dx+a2∫dxx2−a2=12xx2−a2−12a2log⁡x+x2−a2+a2log⁡x+x2−a2+c=12xf(x)+12a2log⁡|x+f(x)|+C
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