Question

recent exam question I need help on
use partial fractions to rewrite this integral as the sum of 9 integrals then stop do not evaluate any of the 9 integrals
int(2/((x-5)^3(x^2+3)^2(x^2+x+9)))dx

Answer 1

\[\frac{2}{(x-5)^3(x^2+3)^2(x^2+x+9)}\]

Answer 2

\[\frac{A}{(x-5)} + \frac{B}{(x-5)^2} + \frac{C}{(x-5)^3} ...\]

Answer 3

Don't know how to write the last 6 parts, but 4 come from (x^2+3)^2 and 2 come from (x^2+x+9)

Answer 4

Once you're done setting that up, you set up an equation and solve for A,B,C,D,E,F,G,H, and I.
May this problem die in a fire. Lols.

Answer 5

\[\frac{-44 x-87}{53508
\left(x^2+3\right)^2}-\frac
{17 (23 x-333)}{116861472
\left(x^2+3\right)}-\frac{2
(x+6)}{59319
\left(x^2+x+9\right)}+\frac
{168913}{4557597408
(x-5)}-\frac{34}{521703
(x-5)^2}+\frac{1}{15288
(x-5)^3}
\]
No one will expect you to do by hand, unless torture is the objective.
Notice that any terms in the denominator that does not have real roots.
Need a term of the form U x + V once or more depending of the power of
the denominator if the term that does not have real roots.

Answer 6

\[
\frac{-44 x-87}{53508
\left(x^2+3\right)^2}-\frac
{17 (23 x-333)}{116861472
\left(x^2+3\right)}-\frac{2
(x+6)}{59319
\left(x^2+x+9\right)}+\\\frac
{168913}{4557597408
(x-5)}-\frac{34}{521703
(x-5)^2}+\frac{1}{15288
(x-5)^3}
\]