Exponential, Logarithmic, Sine, and Cosine Integrals - 6.8 Inequalities

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
6.8.E1	${\displaystyle{\displaystyle\frac{1}{2}\ln\left(1+\frac{2}{x}\right)<e^{x}E_{1}\left(x\right)}}$ \frac{1}{2}\ln@{1+\frac{2}{x}} < e^{x}\expintE@{x}		(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	${\displaystyle{\displaystyle e^{x}E_{1}\left(x\right)<\ln\left(1+\frac{1}{x}\right)}}$ e^{x}\expintE@{x} < \ln@{1+\frac{1}{x}}		exp(x)*Ei(x) < ln(1 +(1)/(x))	Exp[x]*ExpIntegralE[1, x] < Log[1 +Divide[1,x]]	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	${\displaystyle{\displaystyle\frac{x}{x+1}<xe^{x}E_{1}\left(x\right)}}$ \frac{x}{x+1} < xe^{x}\expintE@{x}		(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	${\displaystyle{\displaystyle xe^{x}E_{1}\left(x\right)<\frac{x+1}{x+2}}}$ xe^{x}\expintE@{x} < \frac{x+1}{x+2}		x*exp(x)*Ei(x) < (x + 1)/(x + 2)	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	${\displaystyle{\displaystyle\frac{x(x+3)}{x^{2}+4x+2}<xe^{x}E_{1}\left(x\right)}}$ \frac{x(x+3)}{x^{2}+4x+2} < xe^{x}\expintE@{x}		(x*(x + 3))/((x)^(2)+ 4*x + 2) < x*exp(x)*Ei(x)	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	${\displaystyle{\displaystyle xe^{x}E_{1}\left(x\right)<\frac{x^{2}+5x+2}{x^{2}+6x+6}}}$ xe^{x}\expintE@{x} < \frac{x^{2}+5x+2}{x^{2}+6x+6}		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]