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Q.

∫x2x6+1 is equal to

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a

13x33x6+1+12logx3+x6+1+C

b

13x32x6+1−12logx3+x6+1+C

c

13x32x6+1+12logx+x+1+C

d

13x32x6+1+12logx3+x6+1+C

answer is D.

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Detailed Solution

Let I=∫x2x6+1dx=∫x2x32+1 dx Put x3=tx2dx=dt3I=13∫t2+1dxI=13t2t2+1+12log⁡t+t2+1+C=13x32x6+1+12log⁡x3+x6+1+C
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