## DESCRIPTION
##   Evaluate a Trig Integral
## ENDDESCRIPTION

## KEYWORDS('Indefinite', 'Trig Integral')
## Tagged by nhamblet

## DBsubject('Calculus')
## DBchapter('Techniques of Integration')
## DBsection('Trigonometric Integrals')
## Date('8/23/07')
## Author('K. Lesh')
## Institution('Union')
## TitleText1('Calculus')
## EditionText1('7')
## AuthorText1('Anton')
## Section1('8.3')
## Problem1('08')

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

loadMacros(
  "PGstandard.pl",
  "PGunion.pl",            # Union College utilities
  "MathObjects.pl",
  "PGcourse.pl",           # Customization file for the course
);

TEXT(beginproblem());

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

$n = random(3,9,2);

$integrand=Formula(" tan^{3}(x) sec^{$n}(x)  ");

###################################
# Main text

Context()->texStrings;
BEGIN_TEXT
Evaluate the indefinite integral.
$PAR
\( \displaystyle\int $integrand \, dx \)
             = \{ans_rule(50)\} \( + C\).
END_TEXT
Context()->normalStrings;

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

$showPartialCorrectAnswers = 1;
Context()->flags->set(reduceConstants=>0);

$power2 = $n+2;
$antideriv = Formula(  "(1/$power2)(sec(x))^{$power2} - (1/$n)(sec(x))^$n")
                    ->with(limits => [0,1]);

ANS($antideriv->cmp(upToConstant=>1));

###################################


COMMENT('MathObject version');
ENDDOCUMENT();