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Definite integral

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Evaluate the integral from 0 to infinity of

X^2/(X^4+2X^2+1) dx

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Solution Summary

This shows how to evaluate an integral from zero to infinity.

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I = integral [x^2/(x^4+2x^2+1)] dx
divide by x^2 in numerator and denominator, we get,
I = integral [ 1/{x^2 + 2 + 1/x^2}] dx
=> I = (1/2)*integral [ 2/{x^2 + 2 + 1/x^2}] dx

add and subtract 1/x^2 in numerator,
=> I = (1/2)*integral [ {(1 + 1/x^2) + (1 - 1/x^2)}/{x^2 + 2 + 1/x^2}]dx

Break into two integrals,
=> I = (1/2)*integral[(1 + 1/x^2)/{x^2 + 2 + ...

Solution provided by:
  • BEng, Allahabad University, India
  • MSc , Pune University, India
  • PhD (IP), Pune University, India
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