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### Section 1-8 : Improper Integrals

Determine if each of the following integrals converge or diverge. If the integral converges determine its value.

1. $$\displaystyle \int_{4}^{\infty }{{2 - 4x + 6{x^2}\,dx}}$$
2. $$\displaystyle \int_{0}^{5}{{\frac{1}{{4w - 20}}\,dw}}$$
3. $$\displaystyle \int_{{ - 1}}^{2}{{\frac{3}{{\sqrt{{4 - 2z}}}}\,dz}}$$
4. $$\displaystyle \int_{{ - \infty }}^{0}{{x\,{{\bf{e}}^{2 + 3x}}\,dx}}$$
5. $$\displaystyle \int_{0}^{\infty }{{x\,{{\bf{e}}^{2 + 3x}}\,dx}}$$
6. $$\displaystyle \int_{2}^{\infty }{{\frac{1}{{{x^2} + 1}}\,dx}}$$
7. $$\displaystyle \int_{0}^{3}{{\frac{1}{{{z^2} - 4z}}\,dz}}$$
8. $$\displaystyle \int_{{ - \infty }}^{1}{{\frac{x}{{{x^2} + 1}}\,dx}}$$
9. $$\displaystyle \int_{{ - 1}}^{2}{{\frac{1}{{{y^2} - 2y - 3}}\,dy}}$$
10. $$\displaystyle \int_{{ - \infty }}^{0}{{\cos \left( w \right)\,dw}}$$
11. $$\displaystyle \int_{{10}}^{\infty }{{\frac{1}{{{{\left( {5 - 2z} \right)}^2}}}\,dz}}$$
12. $$\displaystyle \int_{{ - \infty }}^{\infty }{{\frac{{{z^3}}}{{{z^4} + 1}}\,dz}}$$
13. $$\displaystyle \int_{1}^{4}{{\frac{1}{{2y - 6}}\,dy}}$$
14. $$\displaystyle \int_{1}^{5}{{\frac{1}{{\sqrt{{w - 2}}}}\,dw}}$$
15. $$\displaystyle \int_{{ - 2}}^{1}{{\frac{{{{\bf{e}}^{\frac{1}{x}}}}}{{{x^2}}}\,dx}}$$
16. $$\displaystyle \int_{{ - \infty }}^{\infty }{{{x^2}{{\bf{e}}^{{x^{\,3}}}}\,dx}}$$
17. $$\displaystyle \int_{{ - \infty }}^{\infty }{{\frac{y}{{{{\left( {{y^2} + 1} \right)}^3}}}\,dy}}$$
18. $$\displaystyle \int_{0}^{3}{{\frac{{{w^3}}}{{\sqrt {9 - {w^2}} }}\,dw}}$$
19. $$\displaystyle \int_{{ - 3}}^{1}{{\frac{1}{{{w^2} + 2w}}\,dw}}$$
20. $$\displaystyle \int_{0}^{\infty }{{\frac{{{{\bf{e}}^{\frac{1}{x}}}}}{{{x^2}}}\,dx}}$$
21. $$\displaystyle \int_{0}^{\infty }{{\frac{1}{{z{{\left[ {\ln \left( z \right)} \right]}^2}}}\,dz}}$$
22. $$\displaystyle \int_{0}^{\infty }{{\frac{1}{{w - 1}}\,dw}}$$