Evaluate the given integral
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Control-drag the integral.
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Context Panel: Evaluate and Display Inline
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=
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A stepwise solution that uses top-level commands except for one application of the Change command from the IntegrationTools package:
Initialization
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Install the IntegrationTools package.
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Let be the name of the given integral.
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Change variables as per Table 6.3.1
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Use the Change command to apply the change of variables .
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Simplify the radical to . Note the restriction imposed on .
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Apply the half-angle trig identity via the simplify command with the identity as a side relation.
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Split the integral with the expand command, while preventing Maple from applying the double-angle expansion to .
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Use the value command to evaluate what are now two separate but simple integrals.
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Apply the double-angle trig expansion to via the expand command.
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Revert the change of variables by applying the substitution .
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Table 6.3.7(a) displays the annotated stepwise solution provided by the
tutor when the Constant, Constant Multiple, and Sum rules are taken as Understood Rules.
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Table 6.3.7(a) Annotated stepwise solution via Integration Methods tutor
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The essential difference between these two approaches is that Maple's stepwise rules will not permit the integration of without first making the change of variables .
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Note that an annotated stepwise solution is available via the Context Panel with the "All Solution Steps" option.
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The rules of integration can also be applied via the Context Panel, as per the figure to the right.
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