3.72.72 \(\int \frac {e^{e^{x^2}+x^{\frac {1}{x}}} (250 x-500 e^{x^2} x^3+x^{\frac {1}{x}} (-250+250 \log (x)))}{125 e^{3 e^{x^2}+3 x^{\frac {1}{x}}}-1050 e^{2 e^{x^2}+2 x^{\frac {1}{x}}} x+2940 e^{e^{x^2}+x^{\frac {1}{x}}} x^2-2744 x^3} \, dx\)

Optimal. Leaf size=25 \[ \frac {x^2}{\left (e^{e^{x^2}+x^{\frac {1}{x}}}-\frac {14 x}{5}\right )^2} \]

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Rubi [F]  time = 5.01, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {e^{e^{x^2}+x^{\frac {1}{x}}} \left (250 x-500 e^{x^2} x^3+x^{\frac {1}{x}} (-250+250 \log (x))\right )}{125 e^{3 e^{x^2}+3 x^{\frac {1}{x}}}-1050 e^{2 e^{x^2}+2 x^{\frac {1}{x}}} x+2940 e^{e^{x^2}+x^{\frac {1}{x}}} x^2-2744 x^3} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(E^x^2 + x^x^(-1))*(250*x - 500*E^x^2*x^3 + x^x^(-1)*(-250 + 250*Log[x])))/(125*E^(3*E^x^2 + 3*x^x^(-1)
) - 1050*E^(2*E^x^2 + 2*x^x^(-1))*x + 2940*E^(E^x^2 + x^x^(-1))*x^2 - 2744*x^3),x]

[Out]

250*Defer[Int][(E^(E^x^2 + x^x^(-1))*x)/(5*E^(E^x^2 + x^x^(-1)) - 14*x)^3, x] - 500*Defer[Int][(E^(E^x^2 + x^2
+ x^x^(-1))*x^3)/(5*E^(E^x^2 + x^x^(-1)) - 14*x)^3, x] - 250*Defer[Int][(E^(E^x^2 + x^x^(-1))*x^x^(-1))/(5*E^
(E^x^2 + x^x^(-1)) - 14*x)^3, x] + 250*Log[x]*Defer[Int][(E^(E^x^2 + x^x^(-1))*x^x^(-1))/(5*E^(E^x^2 + x^x^(-1
)) - 14*x)^3, x] - 250*Defer[Int][Defer[Int][(E^(E^x^2 + x^x^(-1))*x^x^(-1))/(5*E^(E^x^2 + x^x^(-1)) - 14*x)^3
, x]/x, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {250 e^{e^{x^2}+x^{\frac {1}{x}}} \left (x-2 e^{x^2} x^3-x^{\frac {1}{x}}+x^{\frac {1}{x}} \log (x)\right )}{\left (5 e^{e^{x^2}+x^{\frac {1}{x}}}-14 x\right )^3} \, dx\\ &=250 \int \frac {e^{e^{x^2}+x^{\frac {1}{x}}} \left (x-2 e^{x^2} x^3-x^{\frac {1}{x}}+x^{\frac {1}{x}} \log (x)\right )}{\left (5 e^{e^{x^2}+x^{\frac {1}{x}}}-14 x\right )^3} \, dx\\ &=250 \int \left (-\frac {e^{e^{x^2}+x^{\frac {1}{x}}} x \left (-1+2 e^{x^2} x^2\right )}{\left (5 e^{e^{x^2}+x^{\frac {1}{x}}}-14 x\right )^3}+\frac {e^{e^{x^2}+x^{\frac {1}{x}}} x^{\frac {1}{x}} (-1+\log (x))}{\left (5 e^{e^{x^2}+x^{\frac {1}{x}}}-14 x\right )^3}\right ) \, dx\\ &=-\left (250 \int \frac {e^{e^{x^2}+x^{\frac {1}{x}}} x \left (-1+2 e^{x^2} x^2\right )}{\left (5 e^{e^{x^2}+x^{\frac {1}{x}}}-14 x\right )^3} \, dx\right )+250 \int \frac {e^{e^{x^2}+x^{\frac {1}{x}}} x^{\frac {1}{x}} (-1+\log (x))}{\left (5 e^{e^{x^2}+x^{\frac {1}{x}}}-14 x\right )^3} \, dx\\ &=-\left (250 \int \left (-\frac {e^{e^{x^2}+x^{\frac {1}{x}}} x}{\left (5 e^{e^{x^2}+x^{\frac {1}{x}}}-14 x\right )^3}+\frac {2 e^{e^{x^2}+x^2+x^{\frac {1}{x}}} x^3}{\left (5 e^{e^{x^2}+x^{\frac {1}{x}}}-14 x\right )^3}\right ) \, dx\right )+250 \int \left (-\frac {e^{e^{x^2}+x^{\frac {1}{x}}} x^{\frac {1}{x}}}{\left (5 e^{e^{x^2}+x^{\frac {1}{x}}}-14 x\right )^3}+\frac {e^{e^{x^2}+x^{\frac {1}{x}}} x^{\frac {1}{x}} \log (x)}{\left (5 e^{e^{x^2}+x^{\frac {1}{x}}}-14 x\right )^3}\right ) \, dx\\ &=250 \int \frac {e^{e^{x^2}+x^{\frac {1}{x}}} x}{\left (5 e^{e^{x^2}+x^{\frac {1}{x}}}-14 x\right )^3} \, dx-250 \int \frac {e^{e^{x^2}+x^{\frac {1}{x}}} x^{\frac {1}{x}}}{\left (5 e^{e^{x^2}+x^{\frac {1}{x}}}-14 x\right )^3} \, dx+250 \int \frac {e^{e^{x^2}+x^{\frac {1}{x}}} x^{\frac {1}{x}} \log (x)}{\left (5 e^{e^{x^2}+x^{\frac {1}{x}}}-14 x\right )^3} \, dx-500 \int \frac {e^{e^{x^2}+x^2+x^{\frac {1}{x}}} x^3}{\left (5 e^{e^{x^2}+x^{\frac {1}{x}}}-14 x\right )^3} \, dx\\ &=250 \int \frac {e^{e^{x^2}+x^{\frac {1}{x}}} x}{\left (5 e^{e^{x^2}+x^{\frac {1}{x}}}-14 x\right )^3} \, dx-250 \int \frac {e^{e^{x^2}+x^{\frac {1}{x}}} x^{\frac {1}{x}}}{\left (5 e^{e^{x^2}+x^{\frac {1}{x}}}-14 x\right )^3} \, dx-250 \int \frac {\int \frac {e^{e^{x^2}+x^{\frac {1}{x}}} x^{\frac {1}{x}}}{\left (5 e^{e^{x^2}+x^{\frac {1}{x}}}-14 x\right )^3} \, dx}{x} \, dx-500 \int \frac {e^{e^{x^2}+x^2+x^{\frac {1}{x}}} x^3}{\left (5 e^{e^{x^2}+x^{\frac {1}{x}}}-14 x\right )^3} \, dx+(250 \log (x)) \int \frac {e^{e^{x^2}+x^{\frac {1}{x}}} x^{\frac {1}{x}}}{\left (5 e^{e^{x^2}+x^{\frac {1}{x}}}-14 x\right )^3} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 1.45, size = 26, normalized size = 1.04 \begin {gather*} \frac {25 x^2}{\left (5 e^{e^{x^2}+x^{\frac {1}{x}}}-14 x\right )^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(E^x^2 + x^x^(-1))*(250*x - 500*E^x^2*x^3 + x^x^(-1)*(-250 + 250*Log[x])))/(125*E^(3*E^x^2 + 3*x^
x^(-1)) - 1050*E^(2*E^x^2 + 2*x^x^(-1))*x + 2940*E^(E^x^2 + x^x^(-1))*x^2 - 2744*x^3),x]

[Out]

(25*x^2)/(5*E^(E^x^2 + x^x^(-1)) - 14*x)^2

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fricas [A]  time = 0.69, size = 44, normalized size = 1.76 \begin {gather*} \frac {25 \, x^{2}}{196 \, x^{2} - 140 \, x e^{\left (x^{\left (\frac {1}{x}\right )} + e^{\left (x^{2}\right )}\right )} + 25 \, e^{\left (2 \, x^{\left (\frac {1}{x}\right )} + 2 \, e^{\left (x^{2}\right )}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((250*log(x)-250)*exp(log(x)/x)-500*x^3*exp(x^2)+250*x)*exp(exp(log(x)/x)+exp(x^2))/(125*exp(exp(log
(x)/x)+exp(x^2))^3-1050*x*exp(exp(log(x)/x)+exp(x^2))^2+2940*x^2*exp(exp(log(x)/x)+exp(x^2))-2744*x^3),x, algo
rithm="fricas")

[Out]

25*x^2/(196*x^2 - 140*x*e^(x^(1/x) + e^(x^2)) + 25*e^(2*x^(1/x) + 2*e^(x^2)))

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giac [F(-2)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: NotImplementedError} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((250*log(x)-250)*exp(log(x)/x)-500*x^3*exp(x^2)+250*x)*exp(exp(log(x)/x)+exp(x^2))/(125*exp(exp(log
(x)/x)+exp(x^2))^3-1050*x*exp(exp(log(x)/x)+exp(x^2))^2+2940*x^2*exp(exp(log(x)/x)+exp(x^2))-2744*x^3),x, algo
rithm="giac")

[Out]

Exception raised: NotImplementedError >> Unable to parse Giac output: Exchange 25572169 31 Vector [13,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4] 70 Vector [13,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
,1,1,1,1,1,1,1,4] 70/

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maple [A]  time = 0.10, size = 25, normalized size = 1.00

method	result	size
risch	\(\frac {25 x^{2}}{\left (14 x -5 \,{\mathrm e}^{x^{\frac {1}{x}}+{\mathrm e}^{x^{2}}}\right )^{2}}\)	\(25\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((250*ln(x)-250)*exp(ln(x)/x)-500*x^3*exp(x^2)+250*x)*exp(exp(ln(x)/x)+exp(x^2))/(125*exp(exp(ln(x)/x)+exp
(x^2))^3-1050*x*exp(exp(ln(x)/x)+exp(x^2))^2+2940*x^2*exp(exp(ln(x)/x)+exp(x^2))-2744*x^3),x,method=_RETURNVER
BOSE)

[Out]

25*x^2/(14*x-5*exp(x^(1/x)+exp(x^2)))^2

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maxima [A]  time = 0.49, size = 44, normalized size = 1.76 \begin {gather*} \frac {25 \, x^{2}}{196 \, x^{2} - 140 \, x e^{\left (x^{\left (\frac {1}{x}\right )} + e^{\left (x^{2}\right )}\right )} + 25 \, e^{\left (2 \, x^{\left (\frac {1}{x}\right )} + 2 \, e^{\left (x^{2}\right )}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((250*log(x)-250)*exp(log(x)/x)-500*x^3*exp(x^2)+250*x)*exp(exp(log(x)/x)+exp(x^2))/(125*exp(exp(log
(x)/x)+exp(x^2))^3-1050*x*exp(exp(log(x)/x)+exp(x^2))^2+2940*x^2*exp(exp(log(x)/x)+exp(x^2))-2744*x^3),x, algo
rithm="maxima")

[Out]

25*x^2/(196*x^2 - 140*x*e^(x^(1/x) + e^(x^2)) + 25*e^(2*x^(1/x) + 2*e^(x^2)))

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mupad [B]  time = 4.48, size = 108, normalized size = 4.32 \begin {gather*} -\frac {25\,x^5\,\left (x-2\,x^3\,{\mathrm {e}}^{x^2}-x^{1/x}+x^{1/x}\,\ln \relax (x)\right )}{\left (25\,{\mathrm {e}}^{2\,{\mathrm {e}}^{x^2}+2\,x^{1/x}}-140\,x\,{\mathrm {e}}^{{\mathrm {e}}^{x^2}+x^{1/x}}+196\,x^2\right )\,\left (2\,x^6\,{\mathrm {e}}^{x^2}-x^4+x^{1/x}\,x^3-x^{1/x}\,x^3\,\ln \relax (x)\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(exp(x^2) + exp(log(x)/x))*(250*x - 500*x^3*exp(x^2) + exp(log(x)/x)*(250*log(x) - 250)))/(125*exp(3*e
xp(x^2) + 3*exp(log(x)/x)) - 1050*x*exp(2*exp(x^2) + 2*exp(log(x)/x)) + 2940*x^2*exp(exp(x^2) + exp(log(x)/x))
- 2744*x^3),x)

[Out]

-(25*x^5*(x - 2*x^3*exp(x^2) - x^(1/x) + x^(1/x)*log(x)))/((25*exp(2*exp(x^2) + 2*x^(1/x)) - 140*x*exp(exp(x^2
) + x^(1/x)) + 196*x^2)*(2*x^6*exp(x^2) - x^4 + x^(1/x)*x^3 - x^(1/x)*x^3*log(x)))

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sympy [A]  time = 0.92, size = 44, normalized size = 1.76 \begin {gather*} \frac {x^{2}}{\frac {196 x^{2}}{25} - \frac {28 x e^{e^{x^{2}} + e^{\frac {\log {\relax (x )}}{x}}}}{5} + e^{2 e^{x^{2}} + 2 e^{\frac {\log {\relax (x )}}{x}}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((250*ln(x)-250)*exp(ln(x)/x)-500*x**3*exp(x**2)+250*x)*exp(exp(ln(x)/x)+exp(x**2))/(125*exp(exp(ln(
x)/x)+exp(x**2))**3-1050*x*exp(exp(ln(x)/x)+exp(x**2))**2+2940*x**2*exp(exp(ln(x)/x)+exp(x**2))-2744*x**3),x)

[Out]

x**2/(196*x**2/25 - 28*x*exp(exp(x**2) + exp(log(x)/x))/5 + exp(2*exp(x**2) + 2*exp(log(x)/x)))

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