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Section 7.9 : Comparison Test for Improper Integrals

Use the Comparison Test to determine if the following integrals converge or diverge.

  1. \( \displaystyle \int_{1}^{\infty }{{\frac{1}{{{x^3} + 1}}\,dx}}\) Solution
  2. \( \displaystyle \int_{3}^{\infty }{{\frac{{{z^2}}}{{{z^3} - 1}}\,dz}}\) Solution
  3. \( \displaystyle \int_{4}^{\infty }{{\frac{{{{\bf{e}}^{ - y}}}}{y}\,dy}}\) Solution
  4. \( \displaystyle \int_{1}^{\infty }{{\frac{{z - 1}}{{{z^4} + 2{z^2}}}\,dz}}\) Solution
  5. \( \displaystyle \int_{6}^{\infty }{{\frac{{{w^2} + 1}}{{{w^3}\left( {{{\cos }^2}\left( w \right) + 1} \right)}}\,dw}}\) Solution