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Question

The value of the integral dxx1+xn is:
(where c is integration constant)

A
1nln1+xn1xn+c
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B
1nln1+xn+11xn1+c
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C
1nln1+xn1xn+c
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D
1nln1+xn11+xn+1+c
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Solution

The correct option is D 1nln1+xn11+xn+1+c
Let I=dxx1+xn
Put 1+xn=t2
nxn1dx=2t dtnxndxx=2t dtI=2t dtn(t21)tI=1n2dtt21I=1n(dtt1dtt+1)I=1nlnt1t+1+cI=1nln1+xn11+xn+1+c

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