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Question

x3x+1dx is equal to

(a) x+x22+x33-log1-x+C(b) x+x22-x33-log1-x+C(c) x-x22-x33-log1+x+C(d) x-x22+x33-log1+x+C

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Solution

Let I=x3x+1dx =x3+1-1x+1dx =x3+1x+1-1x+1dx =x+1x2-x+1x+1-1x+1dx =x2-x+1-1x+1dx =x33-x22+x-logx+1+C =x33-x22+x-logx+1+CTherefore, x3x+1dx=x33-x22+x-logx+1+CHence, the correct option is (d).

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