##DESCRIPTION
##KEYWORDS('derivatives', 'antiderivatives')
##  Find an antiderivative of the function
##ENDDESCRIPTION

DOCUMENT();        # This should be the first executable line in the problem.

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

TEXT(&beginproblem);
$showPartialCorrectAnswers = 1;

$a1 = random(2,10,1);
$b1 = random(2,10,1);
$n1 = random(2,3,1);
$m1 = random(5,7,1);
$p1 = random(2,5,1);
TEXT(EV2(<<EOT));
Consider the function \( f(x) = \frac{$a1}{ x^{$n1} } - \frac{$b1}{ x^{$m1} }  \).
$BR
Let \( F(x) \) be the antiderivative of \( f(x) \) with \( F(1) = 0 \).  $BR
Then \( F($p1) \)
equals \{ans_rule(30) \}
EOT
$ans = ($a1/(1-$n1))*$p1**(-$n1+1) - ($b1/(1-$m1))*$p1**(-$m1+1) - ($a1/(1-$n1)) + ($b1/(1-$m1));
&ANS(std_num_cmp($ans));
ENDDOCUMENT();        # This should be the last executable line in the problem.