# 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 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.

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