## DESCRIPTION
## Calculus
## ENDDESCRIPTION

## KEYWORDS('calculus', 'integrals', 'Partial Fractions')
## Tagged by YL

## DBsubject('Calculus')
## DBchapter('Techniques of Integration')
## DBsection('Integration by Partial Fractions')
## Date('')
## Author('')
## Institution('ASU')
## TitleText1('Calculus: Early Transcendentals')
## EditionText1('5')
## AuthorText1('Stewart')
## Section1('7.4')
## Problem1('')

## TitleText2('Calculus: Early Transcendentals')
## EditionText2('6')
## AuthorText2('Stewart')
## Section2('7.4')
## Problem2('')

&DOCUMENT;
loadMacros(
"PG.pl",
"PGbasicmacros.pl",
"PGchoicemacros.pl",
"PGanswermacros.pl",
"PGauxiliaryFunctions.pl"
);


TEXT(beginproblem());

$p=random(1,5,1);
$u=random(1,6,1);
$r=random(-4,-1,1);
$a=random(-3,3,1);
$l=2*$a;
$q=$u+$p*$a;
$b=random(1,5,1);
$c=non_zero_random(-3,3,1);
$d=$p+$r;
$e=$q+($c*$p)+($l*$r);
$k=$a*$a+$b*$b;
$f=($r*$k)+($c*$q);
$g=$l+$c;
$h=$l*$c+$k;
$j=$k*$c;
$hp=$p/2;
$v=$u/$b;
$funct="$hp*ln(x*x+$l*x+$k)+$r*ln(abs(x+$c))+$v*arctan((x+$a)/$b)";

$p1 = nicestring([$d,$e,$f]);
$p2 = nicestring([1,$g,$h,$j]);
TEXT(EV2(<<EOT));

The answer to this question  contains absolute values.$BR
The absolute value of a quantity w should be written abs(w).$BR
Evaluate the integral.
$BR
$BR \[ \int \frac{$p1}{$p2} dx \]
$BR \{ans_rule(80) \}
EOT
$ans=$funct;
ANS(fun_cmp($ans, mode=>"antider"));

&ENDDOCUMENT