Evaluate the given integral
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Control-drag the integral and press the Enter key.
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Context Panel: Simplify≻Simplify
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Context Panel: Expand≻Expand
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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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Impose the trig identity .
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Use the expand command to split the fraction in the integrand into two separate fractions.
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Use the trigsubs command to rewrite as .
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Use the expand command to split the integral into two separate integrals.
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Use the value command to evaluate what are now two separate but relatively simple integrals.
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Revert the change of variables by applying the substitution .
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Table 6.3.8(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 6.3.8(a) First steps of an annotated stepwise solution via Integration Methods tutor
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After the change of variables suggested by Table 6.3.1, Maple returns the integrand as instead of as . Obviously, this saves several manipulative steps. It then takes an application of the Rewrite rule to impose the trig identity , at which point the calculation proceeds as expected.
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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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