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Saturday, November 1, 2008

Q) Find the integral of:

dx / [(x)(1 + x^n)]

A) 1 / [(x)(1 + x^n)]
= (1 + x^n - x^n) / [(x)(1 + x^n)]
= (1/x) - [ (x^n) / {(x)(1 + x^n)} ]
= (1/x) - [ (x^{n-1}) / (1 + x^n) ]
Integrating now:
ln x - ln (1 + x^n) + C
= ln [x / (1 + x^n)] + C

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