text: ## DESCRIPTION
  ## Calculus: The Substitution Rule
  ## ENDDESCRIPTION
  
  ## Tagged by XW
  
  
  ## DBsubject(Calculus - single variable)
  ## DBchapter(Techniques of integration)
  ## DBsection(Substitution (without trigonometric functions))
  ## Date(6/5/2005)
  ## Institution(UVA)
  ## Author(Jeff Holt)
  ## MLT(Sub_direct)
  ## Level(2)
  ## TitleText1('Calculus: Early Transcendentals')
  ## AuthorText1('Stewart')
  ## EditionText1('5')
  ## Section1('5.5')
  ## Problem1('58')
  ## TitleText2('Calculus: Early Transcendentals')
  ## AuthorText2('Stewart')
  ## EditionText2('6')
  ## Section2('5.5')
  ## Problem2('')
  ## KEYWORDS('calculus', 'integrals', 'substitution rule')
  
  DOCUMENT();        # This should be the first executable line in the problem.
  
  loadMacros(
    "PGstandard.pl",
    "PGchoicemacros.pl",
    "PGcourse.pl"
  );
  
  TEXT(beginproblem());
  $showPartialCorrectAnswers = 1;
  
  $a = random(2,4,1);
  $b = $a-1;
  $u = random(1,2,1);
  
  TEXT(EV2(<<EOT));
  Evaluate
  $BR
  \[ \int_{0}^{$u} x^{$b} e^{ -x^{$a} } \, dx . \]
  $BR
  If the integral does not exist, enter DNE.
  $BR
  Definite Integral = \{ ans_rule(35) \}
  $BR
  EOT
  
  $ans = 1/$a * ( 1 - ( exp( -($u**$a) ) ) );
  ANS(num_cmp($ans));
  
  ENDDOCUMENT();        # This should be the last executable line in the problem.
  