3.4.3 \(\int \frac {-25 e^5+25 e^{\frac {2}{25} (625-50 x+x^2)}+e^{5+\frac {1}{25} (625-50 x+x^2)} (50 x-2 x^2)-50 e^{\frac {1}{25} (625-50 x+x^2)} \log (\frac {2}{x})+25 \log ^2(\frac {2}{x})}{25 e^{5+\frac {1}{25} (625-50 x+x^2)} x-25 e^5 x \log (\frac {2}{x})+(25 e^{\frac {2}{25} (625-50 x+x^2)} x-50 e^{\frac {1}{25} (625-50 x+x^2)} x \log (\frac {2}{x})+25 x \log ^2(\frac {2}{x})) \log (x)} \, dx\)

Optimal. Leaf size=32 \[ \log \left (\frac {e^5}{-e^{\left (5-\frac {x}{5}\right )^2}+\log \left (\frac {2}{x}\right )}-\log (x)\right ) \]

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Rubi [F]  time = 28.01, 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 {-25 e^5+25 e^{\frac {2}{25} \left (625-50 x+x^2\right )}+e^{5+\frac {1}{25} \left (625-50 x+x^2\right )} \left (50 x-2 x^2\right )-50 e^{\frac {1}{25} \left (625-50 x+x^2\right )} \log \left (\frac {2}{x}\right )+25 \log ^2\left (\frac {2}{x}\right )}{25 e^{5+\frac {1}{25} \left (625-50 x+x^2\right )} x-25 e^5 x \log \left (\frac {2}{x}\right )+\left (25 e^{\frac {2}{25} \left (625-50 x+x^2\right )} x-50 e^{\frac {1}{25} \left (625-50 x+x^2\right )} x \log \left (\frac {2}{x}\right )+25 x \log ^2\left (\frac {2}{x}\right )\right ) \log (x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-25*E^5 + 25*E^((2*(625 - 50*x + x^2))/25) + E^(5 + (625 - 50*x + x^2)/25)*(50*x - 2*x^2) - 50*E^((625 -
50*x + x^2)/25)*Log[2/x] + 25*Log[2/x]^2)/(25*E^(5 + (625 - 50*x + x^2)/25)*x - 25*E^5*x*Log[2/x] + (25*E^((2*
(625 - 50*x + x^2))/25)*x - 50*E^((625 - 50*x + x^2)/25)*x*Log[2/x] + 25*x*Log[2/x]^2)*Log[x]),x]

[Out]

Log[Log[x]] - Defer[Int][E^(4*x)/(x*(E^((25 + x)^2/25) - E^(4*x)*Log[2/x])), x] - 2*Defer[Int][(E^(4*x)*Log[2/
x])/(-E^((25 + x)^2/25) + E^(4*x)*Log[2/x]), x] + (2*Defer[Int][(E^(4*x)*x*Log[2/x])/(-E^((25 + x)^2/25) + E^(
4*x)*Log[2/x]), x])/25 + 2*Defer[Int][E^(5 + 2*x)/(E^(5 + 2*x) + E^(25 + x^2/25)*Log[x] - E^(2*x)*Log[2/x]*Log
[x]), x] - (2*Defer[Int][(E^(5 + 2*x)*x)/(E^(5 + 2*x) + E^(25 + x^2/25)*Log[x] - E^(2*x)*Log[2/x]*Log[x]), x])
/25 - Defer[Int][E^(5 + 2*x)/(x*Log[x]*(E^(5 + 2*x) + E^(25 + x^2/25)*Log[x] - E^(2*x)*Log[2/x]*Log[x])), x] -
Defer[Int][(E^(2*x)*Log[x])/(x*(-E^(5 + 2*x) - E^(25 + x^2/25)*Log[x] + E^(2*x)*Log[2/x]*Log[x])), x] + 2*Def
er[Int][(E^(2*x)*Log[2/x]*Log[x])/(-E^(5 + 2*x) - E^(25 + x^2/25)*Log[x] + E^(2*x)*Log[2/x]*Log[x]), x] - (2*D
efer[Int][(E^(2*x)*x*Log[2/x]*Log[x])/(-E^(5 + 2*x) - E^(25 + x^2/25)*Log[x] + E^(2*x)*Log[2/x]*Log[x]), x])/2
5

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{4 x} \left (-25 e^5+25 e^{\frac {2}{25} \left (625-50 x+x^2\right )}+e^{5+\frac {1}{25} \left (625-50 x+x^2\right )} \left (50 x-2 x^2\right )-50 e^{\frac {1}{25} \left (625-50 x+x^2\right )} \log \left (\frac {2}{x}\right )+25 \log ^2\left (\frac {2}{x}\right )\right )}{25 x \left (e^{25+\frac {x^2}{25}}-e^{2 x} \log \left (\frac {2}{x}\right )\right ) \left (e^{5+2 x}+e^{25+\frac {x^2}{25}} \log (x)-e^{2 x} \log \left (\frac {2}{x}\right ) \log (x)\right )} \, dx\\ &=\frac {1}{25} \int \frac {e^{4 x} \left (-25 e^5+25 e^{\frac {2}{25} \left (625-50 x+x^2\right )}+e^{5+\frac {1}{25} \left (625-50 x+x^2\right )} \left (50 x-2 x^2\right )-50 e^{\frac {1}{25} \left (625-50 x+x^2\right )} \log \left (\frac {2}{x}\right )+25 \log ^2\left (\frac {2}{x}\right )\right )}{x \left (e^{25+\frac {x^2}{25}}-e^{2 x} \log \left (\frac {2}{x}\right )\right ) \left (e^{5+2 x}+e^{25+\frac {x^2}{25}} \log (x)-e^{2 x} \log \left (\frac {2}{x}\right ) \log (x)\right )} \, dx\\ &=\frac {1}{25} \int \left (-\frac {e^{4 x} \left (25-50 x \log \left (\frac {2}{x}\right )+2 x^2 \log \left (\frac {2}{x}\right )\right )}{x \left (e^{\frac {1}{25} (25+x)^2}-e^{4 x} \log \left (\frac {2}{x}\right )\right )}+\frac {25}{x \log (x)}+\frac {e^{2 x} \left (25 e^5-50 e^5 x \log (x)+2 e^5 x^2 \log (x)-25 \log ^2(x)+50 x \log \left (\frac {2}{x}\right ) \log ^2(x)-2 x^2 \log \left (\frac {2}{x}\right ) \log ^2(x)\right )}{x \log (x) \left (-e^{5+2 x}-e^{25+\frac {x^2}{25}} \log (x)+e^{2 x} \log \left (\frac {2}{x}\right ) \log (x)\right )}\right ) \, dx\\ &=-\left (\frac {1}{25} \int \frac {e^{4 x} \left (25-50 x \log \left (\frac {2}{x}\right )+2 x^2 \log \left (\frac {2}{x}\right )\right )}{x \left (e^{\frac {1}{25} (25+x)^2}-e^{4 x} \log \left (\frac {2}{x}\right )\right )} \, dx\right )+\frac {1}{25} \int \frac {e^{2 x} \left (25 e^5-50 e^5 x \log (x)+2 e^5 x^2 \log (x)-25 \log ^2(x)+50 x \log \left (\frac {2}{x}\right ) \log ^2(x)-2 x^2 \log \left (\frac {2}{x}\right ) \log ^2(x)\right )}{x \log (x) \left (-e^{5+2 x}-e^{25+\frac {x^2}{25}} \log (x)+e^{2 x} \log \left (\frac {2}{x}\right ) \log (x)\right )} \, dx+\int \frac {1}{x \log (x)} \, dx\\ &=-\left (\frac {1}{25} \int \frac {e^{4 x} \left (25+2 (-25+x) x \log \left (\frac {2}{x}\right )\right )}{x \left (e^{\frac {1}{25} (25+x)^2}-e^{4 x} \log \left (\frac {2}{x}\right )\right )} \, dx\right )+\frac {1}{25} \int \left (\frac {50 e^{5+2 x}}{e^{5+2 x}+e^{25+\frac {x^2}{25}} \log (x)-e^{2 x} \log \left (\frac {2}{x}\right ) \log (x)}-\frac {2 e^{5+2 x} x}{e^{5+2 x}+e^{25+\frac {x^2}{25}} \log (x)-e^{2 x} \log \left (\frac {2}{x}\right ) \log (x)}-\frac {25 e^{5+2 x}}{x \log (x) \left (e^{5+2 x}+e^{25+\frac {x^2}{25}} \log (x)-e^{2 x} \log \left (\frac {2}{x}\right ) \log (x)\right )}-\frac {25 e^{2 x} \log (x)}{x \left (-e^{5+2 x}-e^{25+\frac {x^2}{25}} \log (x)+e^{2 x} \log \left (\frac {2}{x}\right ) \log (x)\right )}+\frac {50 e^{2 x} \log \left (\frac {2}{x}\right ) \log (x)}{-e^{5+2 x}-e^{25+\frac {x^2}{25}} \log (x)+e^{2 x} \log \left (\frac {2}{x}\right ) \log (x)}-\frac {2 e^{2 x} x \log \left (\frac {2}{x}\right ) \log (x)}{-e^{5+2 x}-e^{25+\frac {x^2}{25}} \log (x)+e^{2 x} \log \left (\frac {2}{x}\right ) \log (x)}\right ) \, dx+\operatorname {Subst}\left (\int \frac {1}{x} \, dx,x,\log (x)\right )\\ &=\log (\log (x))-\frac {1}{25} \int \left (\frac {25 e^{4 x}}{x \left (e^{\frac {1}{25} (25+x)^2}-e^{4 x} \log \left (\frac {2}{x}\right )\right )}+\frac {50 e^{4 x} \log \left (\frac {2}{x}\right )}{-e^{\frac {1}{25} (25+x)^2}+e^{4 x} \log \left (\frac {2}{x}\right )}-\frac {2 e^{4 x} x \log \left (\frac {2}{x}\right )}{-e^{\frac {1}{25} (25+x)^2}+e^{4 x} \log \left (\frac {2}{x}\right )}\right ) \, dx-\frac {2}{25} \int \frac {e^{5+2 x} x}{e^{5+2 x}+e^{25+\frac {x^2}{25}} \log (x)-e^{2 x} \log \left (\frac {2}{x}\right ) \log (x)} \, dx-\frac {2}{25} \int \frac {e^{2 x} x \log \left (\frac {2}{x}\right ) \log (x)}{-e^{5+2 x}-e^{25+\frac {x^2}{25}} \log (x)+e^{2 x} \log \left (\frac {2}{x}\right ) \log (x)} \, dx+2 \int \frac {e^{5+2 x}}{e^{5+2 x}+e^{25+\frac {x^2}{25}} \log (x)-e^{2 x} \log \left (\frac {2}{x}\right ) \log (x)} \, dx+2 \int \frac {e^{2 x} \log \left (\frac {2}{x}\right ) \log (x)}{-e^{5+2 x}-e^{25+\frac {x^2}{25}} \log (x)+e^{2 x} \log \left (\frac {2}{x}\right ) \log (x)} \, dx-\int \frac {e^{5+2 x}}{x \log (x) \left (e^{5+2 x}+e^{25+\frac {x^2}{25}} \log (x)-e^{2 x} \log \left (\frac {2}{x}\right ) \log (x)\right )} \, dx-\int \frac {e^{2 x} \log (x)}{x \left (-e^{5+2 x}-e^{25+\frac {x^2}{25}} \log (x)+e^{2 x} \log \left (\frac {2}{x}\right ) \log (x)\right )} \, dx\\ &=\log (\log (x))+\frac {2}{25} \int \frac {e^{4 x} x \log \left (\frac {2}{x}\right )}{-e^{\frac {1}{25} (25+x)^2}+e^{4 x} \log \left (\frac {2}{x}\right )} \, dx-\frac {2}{25} \int \frac {e^{5+2 x} x}{e^{5+2 x}+e^{25+\frac {x^2}{25}} \log (x)-e^{2 x} \log \left (\frac {2}{x}\right ) \log (x)} \, dx-\frac {2}{25} \int \frac {e^{2 x} x \log \left (\frac {2}{x}\right ) \log (x)}{-e^{5+2 x}-e^{25+\frac {x^2}{25}} \log (x)+e^{2 x} \log \left (\frac {2}{x}\right ) \log (x)} \, dx-2 \int \frac {e^{4 x} \log \left (\frac {2}{x}\right )}{-e^{\frac {1}{25} (25+x)^2}+e^{4 x} \log \left (\frac {2}{x}\right )} \, dx+2 \int \frac {e^{5+2 x}}{e^{5+2 x}+e^{25+\frac {x^2}{25}} \log (x)-e^{2 x} \log \left (\frac {2}{x}\right ) \log (x)} \, dx+2 \int \frac {e^{2 x} \log \left (\frac {2}{x}\right ) \log (x)}{-e^{5+2 x}-e^{25+\frac {x^2}{25}} \log (x)+e^{2 x} \log \left (\frac {2}{x}\right ) \log (x)} \, dx-\int \frac {e^{4 x}}{x \left (e^{\frac {1}{25} (25+x)^2}-e^{4 x} \log \left (\frac {2}{x}\right )\right )} \, dx-\int \frac {e^{5+2 x}}{x \log (x) \left (e^{5+2 x}+e^{25+\frac {x^2}{25}} \log (x)-e^{2 x} \log \left (\frac {2}{x}\right ) \log (x)\right )} \, dx-\int \frac {e^{2 x} \log (x)}{x \left (-e^{5+2 x}-e^{25+\frac {x^2}{25}} \log (x)+e^{2 x} \log \left (\frac {2}{x}\right ) \log (x)\right )} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [F]  time = 0.49, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {-25 e^5+25 e^{\frac {2}{25} \left (625-50 x+x^2\right )}+e^{5+\frac {1}{25} \left (625-50 x+x^2\right )} \left (50 x-2 x^2\right )-50 e^{\frac {1}{25} \left (625-50 x+x^2\right )} \log \left (\frac {2}{x}\right )+25 \log ^2\left (\frac {2}{x}\right )}{25 e^{5+\frac {1}{25} \left (625-50 x+x^2\right )} x-25 e^5 x \log \left (\frac {2}{x}\right )+\left (25 e^{\frac {2}{25} \left (625-50 x+x^2\right )} x-50 e^{\frac {1}{25} \left (625-50 x+x^2\right )} x \log \left (\frac {2}{x}\right )+25 x \log ^2\left (\frac {2}{x}\right )\right ) \log (x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[(-25*E^5 + 25*E^((2*(625 - 50*x + x^2))/25) + E^(5 + (625 - 50*x + x^2)/25)*(50*x - 2*x^2) - 50*E^((
625 - 50*x + x^2)/25)*Log[2/x] + 25*Log[2/x]^2)/(25*E^(5 + (625 - 50*x + x^2)/25)*x - 25*E^5*x*Log[2/x] + (25*
E^((2*(625 - 50*x + x^2))/25)*x - 50*E^((625 - 50*x + x^2)/25)*x*Log[2/x] + 25*x*Log[2/x]^2)*Log[x]),x]

[Out]

Integrate[(-25*E^5 + 25*E^((2*(625 - 50*x + x^2))/25) + E^(5 + (625 - 50*x + x^2)/25)*(50*x - 2*x^2) - 50*E^((
625 - 50*x + x^2)/25)*Log[2/x] + 25*Log[2/x]^2)/(25*E^(5 + (625 - 50*x + x^2)/25)*x - 25*E^5*x*Log[2/x] + (25*
E^((2*(625 - 50*x + x^2))/25)*x - 50*E^((625 - 50*x + x^2)/25)*x*Log[2/x] + 25*x*Log[2/x]^2)*Log[x]), x]

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fricas [B]  time = 0.81, size = 81, normalized size = 2.53 \begin {gather*} \log \left (e^{5} \log \left (\frac {2}{x}\right )^{2} + e^{\left (\frac {1}{25} \, x^{2} - 2 \, x + 30\right )} \log \relax (2) - {\left (e^{5} \log \relax (2) + e^{\left (\frac {1}{25} \, x^{2} - 2 \, x + 30\right )}\right )} \log \left (\frac {2}{x}\right ) + e^{10}\right ) - \log \left (e^{5} \log \left (\frac {2}{x}\right ) - e^{\left (\frac {1}{25} \, x^{2} - 2 \, x + 30\right )}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((25*log(2/x)^2-50*exp(1/25*x^2-2*x+25)*log(2/x)+25*exp(1/25*x^2-2*x+25)^2+(-2*x^2+50*x)*exp(5)*exp(1
/25*x^2-2*x+25)-25*exp(5))/((25*x*log(2/x)^2-50*x*exp(1/25*x^2-2*x+25)*log(2/x)+25*x*exp(1/25*x^2-2*x+25)^2)*l
og(x)-25*x*exp(5)*log(2/x)+25*x*exp(5)*exp(1/25*x^2-2*x+25)),x, algorithm="fricas")

[Out]

log(e^5*log(2/x)^2 + e^(1/25*x^2 - 2*x + 30)*log(2) - (e^5*log(2) + e^(1/25*x^2 - 2*x + 30))*log(2/x) + e^10)
- log(e^5*log(2/x) - e^(1/25*x^2 - 2*x + 30))

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giac [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((25*log(2/x)^2-50*exp(1/25*x^2-2*x+25)*log(2/x)+25*exp(1/25*x^2-2*x+25)^2+(-2*x^2+50*x)*exp(5)*exp(1
/25*x^2-2*x+25)-25*exp(5))/((25*x*log(2/x)^2-50*x*exp(1/25*x^2-2*x+25)*log(2/x)+25*x*exp(1/25*x^2-2*x+25)^2)*l
og(x)-25*x*exp(5)*log(2/x)+25*x*exp(5)*exp(1/25*x^2-2*x+25)),x, algorithm="giac")

[Out]

Timed out

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maple [C]  time = 0.77, size = 52, normalized size = 1.62

method	result	size
risch	\(-\ln \left (\ln \relax (x )+\frac {i \left (2 i \ln \relax (2)-2 i {\mathrm e}^{\frac {\left (x -25\right )^{2}}{25}}\right )}{2}\right )+\ln \left (\ln \relax (x )^{2}+\left ({\mathrm e}^{\frac {\left (x -25\right )^{2}}{25}}-\ln \relax (2)\right ) \ln \relax (x )+{\mathrm e}^{5}\right )\)	\(52\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((25*ln(2/x)^2-50*exp(1/25*x^2-2*x+25)*ln(2/x)+25*exp(1/25*x^2-2*x+25)^2+(-2*x^2+50*x)*exp(5)*exp(1/25*x^2-
2*x+25)-25*exp(5))/((25*x*ln(2/x)^2-50*x*exp(1/25*x^2-2*x+25)*ln(2/x)+25*x*exp(1/25*x^2-2*x+25)^2)*ln(x)-25*x*
exp(5)*ln(2/x)+25*x*exp(5)*exp(1/25*x^2-2*x+25)),x,method=_RETURNVERBOSE)

[Out]

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

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maxima [B]  time = 0.54, size = 77, normalized size = 2.41 \begin {gather*} -\log \left (-{\left ({\left (\log \relax (2) - \log \relax (x)\right )} e^{\left (2 \, x\right )} - e^{\left (\frac {1}{25} \, x^{2} + 25\right )}\right )} e^{\left (-25\right )}\right ) + \log \left (-\frac {{\left ({\left (\log \relax (2) \log \relax (x) - \log \relax (x)^{2} - e^{5}\right )} e^{\left (2 \, x\right )} - e^{\left (\frac {1}{25} \, x^{2} + 25\right )} \log \relax (x)\right )} e^{\left (-25\right )}}{\log \relax (x)}\right ) + \log \left (\log \relax (x)\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((25*log(2/x)^2-50*exp(1/25*x^2-2*x+25)*log(2/x)+25*exp(1/25*x^2-2*x+25)^2+(-2*x^2+50*x)*exp(5)*exp(1
/25*x^2-2*x+25)-25*exp(5))/((25*x*log(2/x)^2-50*x*exp(1/25*x^2-2*x+25)*log(2/x)+25*x*exp(1/25*x^2-2*x+25)^2)*l
og(x)-25*x*exp(5)*log(2/x)+25*x*exp(5)*exp(1/25*x^2-2*x+25)),x, algorithm="maxima")

[Out]

-log(-((log(2) - log(x))*e^(2*x) - e^(1/25*x^2 + 25))*e^(-25)) + log(-((log(2)*log(x) - log(x)^2 - e^5)*e^(2*x
) - e^(1/25*x^2 + 25)*log(x))*e^(-25)/log(x)) + log(log(x))

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {25\,{\ln \left (\frac {2}{x}\right )}^2-50\,{\mathrm {e}}^{\frac {x^2}{25}-2\,x+25}\,\ln \left (\frac {2}{x}\right )-25\,{\mathrm {e}}^5+25\,{\mathrm {e}}^{\frac {2\,x^2}{25}-4\,x+50}+{\mathrm {e}}^{\frac {x^2}{25}-2\,x+30}\,\left (50\,x-2\,x^2\right )}{\ln \relax (x)\,\left (25\,x\,{\ln \left (\frac {2}{x}\right )}^2-50\,x\,{\mathrm {e}}^{\frac {x^2}{25}-2\,x+25}\,\ln \left (\frac {2}{x}\right )+25\,x\,{\mathrm {e}}^{\frac {2\,x^2}{25}-4\,x+50}\right )+25\,x\,{\mathrm {e}}^{\frac {x^2}{25}-2\,x+30}-25\,x\,{\mathrm {e}}^5\,\ln \left (\frac {2}{x}\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((25*exp((2*x^2)/25 - 4*x + 50) - 25*exp(5) + 25*log(2/x)^2 - 50*exp(x^2/25 - 2*x + 25)*log(2/x) + exp(5)*e
xp(x^2/25 - 2*x + 25)*(50*x - 2*x^2))/(log(x)*(25*x*exp((2*x^2)/25 - 4*x + 50) + 25*x*log(2/x)^2 - 50*x*exp(x^
2/25 - 2*x + 25)*log(2/x)) + 25*x*exp(5)*exp(x^2/25 - 2*x + 25) - 25*x*exp(5)*log(2/x)),x)

[Out]

int((25*exp((2*x^2)/25 - 4*x + 50) - 25*exp(5) + 25*log(2/x)^2 + exp(x^2/25 - 2*x + 30)*(50*x - 2*x^2) - 50*ex
p(x^2/25 - 2*x + 25)*log(2/x))/(log(x)*(25*x*exp((2*x^2)/25 - 4*x + 50) + 25*x*log(2/x)^2 - 50*x*exp(x^2/25 -
2*x + 25)*log(2/x)) + 25*x*exp(x^2/25 - 2*x + 30) - 25*x*exp(5)*log(2/x)), x)

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sympy [B]  time = 2.11, size = 76, normalized size = 2.38 \begin {gather*} - \log {\left (\frac {2 \log {\relax (x )}^{2} - 2 \log {\relax (2 )} \log {\relax (x )}}{2 \log {\relax (x )}} + e^{\frac {x^{2}}{25} - 2 x + 25} \right )} + \log {\left (\frac {2 \log {\relax (x )}^{2} - 2 \log {\relax (2 )} \log {\relax (x )} + 2 e^{5}}{2 \log {\relax (x )}} + e^{\frac {x^{2}}{25} - 2 x + 25} \right )} + \log {\left (\log {\relax (x )} \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((25*ln(2/x)**2-50*exp(1/25*x**2-2*x+25)*ln(2/x)+25*exp(1/25*x**2-2*x+25)**2+(-2*x**2+50*x)*exp(5)*ex
p(1/25*x**2-2*x+25)-25*exp(5))/((25*x*ln(2/x)**2-50*x*exp(1/25*x**2-2*x+25)*ln(2/x)+25*x*exp(1/25*x**2-2*x+25)
**2)*ln(x)-25*x*exp(5)*ln(2/x)+25*x*exp(5)*exp(1/25*x**2-2*x+25)),x)

[Out]

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

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