Partial Fractions Summary $(15$ pts$)$

Please note that each of the first $3$ problems are worth $2$ points, $4-6$ are worth $2\mathrm{.}5$ points and the last is worth $3.$ This means you have $16\mathrm{.}5$ points on offer, but the grade will be out of $15.$

You may use any notes or external references you want, and can even converse with one another, but the work you submit to me must be your own $($i$.$e$.$ do not copy others or use calculators$)!$

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

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{3x^2+3x-6}{(x+1)(x-2{)}^2}dx$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{x^2-3x-5}{(x-1{)}^3}dx$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{x^3+6x-4}{x^2(x+1)(x-1)}dx$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{5x+3}{4x^3+x}dx$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{x^3+2x^2+3x+4}{x^4+2x^2}dx$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{10x+4}{(x+2)(x^2+8x+20)}dx$