 Warning, unable to determine if ... is between ... and ...; try to use assumptions or use the AllSolutions option - Maple Programming Help

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Warning, unable to determine if ... is between ... and ...; try to use assumptions or use the AllSolutions option

 Description This warning appears only when the result will be piecewise due to one or more unknowns in the expression. Ideally, you should use assumptions, but sometimes you cannot determine the right assumptions. When you use the AllSolutions option, Maple assumes that all parameters are real and will try to return an piecewise answer, which covers all possible cases. By using the AllSolutions option, you can use the piecewise answer to determine what assumptions you must make on the parameters. Note: The answer is likely to be large and it may take longer to compute this answer.

Examples

 > ${∫}_{1}^{b}\frac{1}{x-a}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}ⅆx$
 ${{∫}}_{{1}}^{{b}}\frac{{1}}{{x}{-}{a}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{x}$ (2.1)
 >
 ${{∫}}_{{1}}^{{b}}\frac{{1}}{{x}{-}{a}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{x}$ (2.2)

Solution 1: Use assumptions.

 >
 ${\mathrm{undefined}}$ (2.3)
 >
 ${-}{\mathrm{ln}}{\mathit{}}\left({a}{-}{1}\right){+}{\mathrm{ln}}{\mathit{}}\left({a}{-}{b}\right)$ (2.4)

Solution 2: Use the AllSolutions option.

By using the AllSolutions option, int returns the entire set of solutions for the specified definite integral. This applies primarily to parameters in the endpoints of the interval, not to parameters in the integrand.

Note: To specify options, use the int calling sequence.

 >
 ${{}\begin{array}{cc}{{}\begin{array}{cc}{\mathrm{undefined}}& {\mathrm{And}}{\mathit{}}\left({1}{<}{\mathrm{ℜ}}{\mathit{}}\left({a}\right){,}{\mathrm{ℜ}}{\mathit{}}\left({a}\right){<}{b}\right)\\ \left({{}\begin{array}{cc}{\mathrm{∞}}& {a}{=}{1}\\ {-}{\mathrm{ln}}{\mathit{}}\left({a}{-}{1}\right)& {\mathrm{otherwise}}\end{array}\right){+}\left({{}\begin{array}{cc}{-}{\mathrm{∞}}& {b}{=}{a}\\ {\mathrm{ln}}{\mathit{}}\left({a}{-}{b}\right)& {\mathrm{otherwise}}\end{array}\right)& {\mathrm{otherwise}}\end{array}& {1}{<}{b}\\ {0}& {b}{=}{1}\\ {-}\left({{}\begin{array}{cc}{\mathrm{undefined}}& {\mathrm{And}}{\mathit{}}\left({b}{<}{\mathrm{ℜ}}{\mathit{}}\left({a}\right){,}{\mathrm{ℜ}}{\mathit{}}\left({a}\right){<}{1}\right)\\ {-}\left({{}\begin{array}{cc}{-}{\mathrm{∞}}& {b}{=}{a}\\ {\mathrm{ln}}{\mathit{}}\left({a}{-}{b}\right)& {\mathrm{otherwise}}\end{array}\right){+}\left({{}\begin{array}{cc}{-}{\mathrm{∞}}& {a}{=}{1}\\ {\mathrm{ln}}{\mathit{}}\left({a}{-}{1}\right)& {\mathrm{otherwise}}\end{array}\right)& {\mathrm{otherwise}}\end{array}\right)& {b}{<}{1}\end{array}$ (2.5)