Problem $21.$ Use integration by partial fraction decomposition to evaluate the integrals.

$($a$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{dx}{1-x^2}$

$($g$)\frac{dx}{((x^2-1){)}^2}$

$($b$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{x+4}{x^2+5x-6}dx$

$($h$){\displaystyle \underset{0}{\overset{1}{}}}\frac{dx}{(x+1)(x^2+1)}$

$($c$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{dx}{x^2+2x}$

$($i$){\displaystyle \underset{1}{\overset{\sqrt[\phantom{2}]{3}}{}}}\frac{3x^2+x+4}{x^3+x}dx$

$($d$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{2x+1}{x^2-7x+12}dx$

$($j$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{t^2+2t+1}{(t^2+1{)}^2}dt$

$($e$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{x+3}{2x^3-8x}dx$

$($k$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{2x^3-2x^2+1}{x^2-x}dx$

$($f$){\displaystyle \underset{0}{\overset{1}{}}}\frac{x^3}{x^2+2x+1}dx$

$($l$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{x^4}{x^2-1}dx$