##DESCRIPTION
##KEYWORDS('integrals', 'trigonometric','substitution')
##ENDDESCRIPTION

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

loadMacros(
"PGstandard.pl",
"PGcourse.pl",
"MathObjects.pl",
# "source.pl",
);

TEXT(beginproblem());
$showPartialCorrectAnswers = 1;

###################
#
#  Setup

$a = random(1,10,1);
$b = random(1,6,1);
$c1 = random(2,6,1);
$c = $b+$c1;
$d = random(2,100,1);
$a1 = $c*$c-$b*$b;
$a2 = $a*$a;
$ab2 = 2*$a*$b;

# The answer checker needs to be given a domain for this antiderivative to prevent it testing values for x such that the antiderivative is undefined.
   $rend = $c1/$a;
   $lend = 0;

$Funct = Formula("$d/sqrt($a1 - $ab2 x - $a2 x^2)")->reduce;
$Antideriv = Formula("$d*arcsin(($a*x+ $b)/$c)/$a ");

###################
#
#  Text

Context()->texStrings;
BEGIN_TEXT

Evaluate the indefinite integral.
$PAR \[ \int $Funct dx \]
$BR \{ans_rule(30) \}

END_TEXT
Context()->normalStrings;

###################
#
#  Answers

ANS($Antideriv->cmp(domain=>[$lend,$rend]),(upToConstant=>1));
   # domain: makes sure that test points only lie in a certain interval, this 
   # is useful for antiderivatives or general functions with restricted domains.
 
   # upToConstant: Checks student's formula up to a constant, essentially asking 
   # the student to find 'an' antiderivative.  
    
   # For example, given Int(x^2), both (x^3)/3 and (x^3)/3 + 9 would both be
   # marked correct.

ENDDOCUMENT();        # This should be the last executable line in the problem.