Exponential, Logarithmic, Sine, and Cosine Integrals - 6.8 Inequalities
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| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 6.8.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{2}\ln@{1+\frac{2}{x}} < e^{x}\expintE@{x}}
\frac{1}{2}\ln@{1+\frac{2}{x}} < e^{x}\expintE@{x} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (1)/(2)*ln(1 +(2)/(x)) < exp(x)*Ei(x)
|
Divide[1,2]*Log[1 +Divide[2,x]] < Exp[x]*ExpIntegralE[1, x]
|
Failure | Failure | Failed [1 / 3] Result: .8047189560 < .7488820189
Test Values: {x = .5}
|
Successful [Tested: 3] |
| 6.8.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{x}\expintE@{x} < \ln@{1+\frac{1}{x}}}
e^{x}\expintE@{x} < \ln@{1+\frac{1}{x}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | exp(x)*Ei(x) < ln(1 +(1)/(x))
|
Exp[x]*ExpIntegralE[1, x] < Log[1 +Divide[1,x]]
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Failure | Failure | Failed [2 / 3] Result: 14.79533491 < .5108256240
Test Values: {x = 1.5}
Result: 36.60711558 < .4054651081
Test Values: {x = 2}
|
Successful [Tested: 3] |
| 6.8.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{x}{x+1} < xe^{x}\expintE@{x}}
\frac{x}{x+1} < xe^{x}\expintE@{x} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (x)/(x + 1) < x*exp(x)*Ei(x)
|
Divide[x,x + 1] < x*Exp[x]*ExpIntegralE[1, x]
|
Failure | Failure | Successful [Tested: 3] | Successful [Tested: 3] |
| 6.8.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle xe^{x}\expintE@{x} < \frac{x+1}{x+2}}
xe^{x}\expintE@{x} < \frac{x+1}{x+2} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | x*exp(x)*Ei(x) < (x + 1)/(x + 2)
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x*Exp[x]*ExpIntegralE[1, x] < Divide[x + 1,x + 2]
|
Failure | Failure | Failed [2 / 3] Result: 22.19300237 < .7142857143
Test Values: {x = 1.5}
Result: 73.21423116 < .7500000000
Test Values: {x = 2}
|
Successful [Tested: 3] |
| 6.8.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{x(x+3)}{x^{2}+4x+2} < xe^{x}\expintE@{x}}
\frac{x(x+3)}{x^{2}+4x+2} < xe^{x}\expintE@{x} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (x*(x + 3))/((x)^(2)+ 4*x + 2) < x*exp(x)*Ei(x)
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Divide[x*(x + 3),(x)^(2)+ 4*x + 2] < x*Exp[x]*ExpIntegralE[1, x]
|
Failure | Failure | Failed [1 / 3] Result: .4117647059 < .3744410095
Test Values: {x = .5}
|
Successful [Tested: 3] |
| 6.8.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle xe^{x}\expintE@{x} < \frac{x^{2}+5x+2}{x^{2}+6x+6}}
xe^{x}\expintE@{x} < \frac{x^{2}+5x+2}{x^{2}+6x+6} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | x*exp(x)*Ei(x) < ((x)^(2)+ 5*x + 2)/((x)^(2)+ 6*x + 6)
|
x*Exp[x]*ExpIntegralE[1, x] < Divide[(x)^(2)+ 5*x + 2,(x)^(2)+ 6*x + 6]
|
Failure | Failure | Failed [2 / 3] Result: 22.19300237 < .6811594203
Test Values: {x = 1.5}
Result: 73.21423116 < .7272727273
Test Values: {x = 2}
|
Successful [Tested: 3] |