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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

    © BrainMass Inc. brainmass.com March 4, 2021, 6:08 pm ad1c9bdddf
    https://brainmass.com/math/integrals/definite-integral-31087

    Solution Preview

    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 Summary

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

    $2.19

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