Apêndice A
Tabelas

Tabela de integrais definidas, ver [?]):

1. ${\mathrm{\int \; <!--nolimits-->}<!--FUNCTION\; APPLICATION-->}_0^{\infty }{e}^{-ax}\cos <!--FUNCTION\; APPLICATION-->\left(mx\right)dx=\frac{a}{a^2+m^2}\left(a>0\right)$
2. ${\mathrm{\int \; <!--nolimits-->}<!--FUNCTION\; APPLICATION-->}_0^{\infty }{e}^{-ax}\mathrm{sen}<!--FUNCTION\; APPLICATION-->\left(mx\right)dx=\frac{m}{a^2+m^2}\left(a>0\right)$
3. ${\mathrm{\int \; <!--nolimits-->}<!--FUNCTION\; APPLICATION-->}_0^{\infty }\frac{\cos <!--FUNCTION\; APPLICATION-->\left(mx\right)}{a^2+x^2}dx=\frac{\pi }{2a}{e}^{-ma}\left(a>0,m\ge 0\right)$
4. ${\mathrm{\int \; <!--nolimits-->}<!--FUNCTION\; APPLICATION-->}_0^{\infty }\frac{x\mathrm{sen}<!--FUNCTION\; APPLICATION-->\left(mx\right)}{a^2+x^2}dx=\frac{\pi }{2}{e}^{-ma}\left(a\ge 0,m>0\right)$
5. ${\mathrm{\int \; <!--nolimits-->}<!--FUNCTION\; APPLICATION-->}_0^{\infty }\frac{\mathrm{sen}<!--FUNCTION\; APPLICATION-->\left(mx\right)\cos <!--FUNCTION\; APPLICATION-->\left(nx\right)}{x}dx=\left\{\begin{array}{c}\frac{\pi }{2},n<m\hfill \\ \frac{\pi }{4},n=m,\left(m>0,n>0\right)\hfill \\ 0,n>m\hfill \end{array}\right.$
6. ${\mathrm{\int \; <!--nolimits-->}<!--FUNCTION\; APPLICATION-->}_0^{\infty }\frac{\mathrm{sen}<!--FUNCTION\; APPLICATION-->\left(mx\right)}{x}dx=\left\{\begin{array}{c}\frac{\pi }{2},m>0\hfill \\ 0,m=0\hfill \\ -\frac{\pi }{2},m<0\hfill \end{array}\right.$
7. ${\mathrm{\int \; <!--nolimits-->}<!--FUNCTION\; APPLICATION-->}_0^{\infty }{e}^{-r^2{x}^2}dx=\frac{\sqrt{\pi }}{2r}\left(r>0\right)$
8. ${\mathrm{\int \; <!--nolimits-->}<!--FUNCTION\; APPLICATION-->}_0^{\infty }{e}^{-a^2{x}^2}\cos <!--FUNCTION\; APPLICATION-->\left(mx\right)dx=\frac{\sqrt{\pi }}{2a}{e}^{-\frac{m^2}{4a^2}}\left(a>0\right)$
9. ${\mathrm{\int \; <!--nolimits-->}<!--FUNCTION\; APPLICATION-->}_0^{\infty }x{e}^{-ax}\mathrm{sen}<!--FUNCTION\; APPLICATION-->\left(mx\right)dx=\frac{2am}{{\left(a^2+m^2\right)}^2}\left(a>0\right)$
10. ${\mathrm{\int \; <!--nolimits-->}<!--FUNCTION\; APPLICATION-->}_0^{\infty }{e}^{-ax}\mathrm{sen}<!--FUNCTION\; APPLICATION-->\left(mx\right)\cos <!--FUNCTION\; APPLICATION-->\left(nx\right)dx=\frac{m\left(a^2+m^2-n^2\right)}{\left(a^2+{\left(m-n\right)}^2\right)\left(a^2+{\left(m+n\right)}^2\right)}\left(a>0\right)$
11. ${\mathrm{\int \; <!--nolimits-->}<!--FUNCTION\; APPLICATION-->}_0^{\infty }x{e}^{-ax}\cos <!--FUNCTION\; APPLICATION-->\left(mx\right)dx=\frac{a^2-m^2}{{\left(a^2+m^2\right)}^2}\left(a>0\right)$
12. ${\mathrm{\int \; <!--nolimits-->}<!--FUNCTION\; APPLICATION-->}_0^{\infty }\frac{\cos <!--FUNCTION\; APPLICATION-->\left(mx\right)}{x^4+4a^4}dx=\frac{\pi }{8a^3}{e}^{-ma}\left(\mathrm{sen}<!--FUNCTION\; APPLICATION-->\left(ma\right)+\cos <!--FUNCTION\; APPLICATION-->\left(ma\right)\right)$
13. ${\mathrm{\int \; <!--nolimits-->}<!--FUNCTION\; APPLICATION-->}_0^{\infty }\frac{\mathrm{sen}<!--FUNCTION\; APPLICATION-->{}^2\left(mx\right)}{x^2}dx=\left|m\right|\frac{\pi }{2}$
14. $\mathrm{erf}<!--FUNCTION\; APPLICATION-->\left(x\right)=\frac{2}{\sqrt{\pi }}{\mathrm{\int \; <!--nolimits-->}<!--FUNCTION\; APPLICATION-->}_0^x{e}^{-z^2}dz$
15. ${\mathrm{\int \; <!--nolimits-->}<!--FUNCTION\; APPLICATION-->}_0^{\infty }\frac{\mathrm{sen}<!--FUNCTION\; APPLICATION-->{}^2\left(ax\right)\mathrm{sen}<!--FUNCTION\; APPLICATION-->\left(mx\right)}{x}dx=\left\{\begin{array}{c}\frac{\pi }{4},\left(0<m<2a\right)\hfill \\ \hfill \\ \frac{\pi }{8},\left(0<2a=m\right)\hfill \\ \hfill \\ 0,\left(0<2a<m\right)\hfill \end{array}\right.$
16. ${\mathrm{\int \; <!--nolimits-->}<!--FUNCTION\; APPLICATION-->}_0^{\infty }\frac{\mathrm{sen}<!--FUNCTION\; APPLICATION-->\left(mx\right)\mathrm{sen}<!--FUNCTION\; APPLICATION-->\left(nx\right)}{x^2}dx=\left\{\begin{array}{c}\frac{\pi m}{2},\left(0<m\le n\right)\hfill \\ \hfill \\ \frac{\pi n}{2},\left(0<n\le m\right)\hfill \end{array}\right.$
17. ${\mathrm{\int \; <!--nolimits-->}<!--FUNCTION\; APPLICATION-->}_0^{\infty }{x}^2{e}^{-ax}\mathrm{sen}<!--FUNCTION\; APPLICATION-->\left(mx\right)dx=\frac{2m\left(3a^2-m^2\right)}{{\left(a^2+m^2\right)}^3}\left(a>0\right)$
18. ${\mathrm{\int \; <!--nolimits-->}<!--FUNCTION\; APPLICATION-->}_0^{\infty }{x}^2{e}^{-ax}\cos <!--FUNCTION\; APPLICATION-->\left(mx\right)dx=\frac{2a\left(a^2-3m^2\right)}{{\left(a^2+m^2\right)}^3}\left(a>0\right)$
19. ${\mathrm{\int \; <!--nolimits-->}<!--FUNCTION\; APPLICATION-->}_0^{\infty }\frac{\cos <!--FUNCTION\; APPLICATION-->\left(mx\right)}{{\left(a^2+x^2\right)}^2}dx=\frac{\pi }{4a^3}\left(1+ma\right)e^{-ma}\begin{array}{c}(a>0,\hfill \\ m\ge 0)\hfill \end{array}$
20. ${\mathrm{\int \; <!--nolimits-->}<!--FUNCTION\; APPLICATION-->}_0^{\infty }\frac{x\mathrm{sen}<!--FUNCTION\; APPLICATION-->\left(mx\right)}{{\left(a^2+x^2\right)}^2}dx=\frac{\pi m}{4a}{e}^{-ma}\left(a>0,m>0\right)$
21. ${\mathrm{\int \; <!--nolimits-->}<!--FUNCTION\; APPLICATION-->}_0^{\infty }\frac{x^2\cos <!--FUNCTION\; APPLICATION-->\left(mx\right)}{{\left(a^2+x^2\right)}^2}dx=\frac{\pi }{4a}\left(1-ma\right)e^{-ma}\begin{array}{c}(a>0,\hfill \\ m\ge 0)\hfill \end{array}$
22. ${\mathrm{\int \; <!--nolimits-->}<!--FUNCTION\; APPLICATION-->}_0^{\infty }x{e}^{-a^2{x}^2}\mathrm{sen}<!--FUNCTION\; APPLICATION-->\left(mx\right)dx=\frac{m\sqrt{\pi }}{4a^3}{e}^{-\frac{m^2}{4a^2}}\left(a>0\right)$