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Evaluating integrals

I'm taking a DE calculus class and I'm having problems figuring out the logic in solving some of the problems.

The given integral is improper because both the interval of integration is unbounded and the integrand is unbounded near zero. Investigate its convergence by expressing it a sum of two intergrands-one from 0 to 1 and one from 1 to infinity. Evaluate the integrals if they converge.

1/(x^2/3 + x^4/3) dx

Solution Preview

Solution. Since 1/(x^2/3+x^4/3)=3/(x^2+x^4)=3{1/x^2-1/(x^2+1)}
<br>We know that if the integrand f(x)=1/(x^2+1), then integrate x from 0 to infinity, the ...