3.48.50 \(\int \frac {-2 e^{679} x^2 \log (2)+2 x \log (2) \log (x)+(-2 \log (2)+2 \log (2) \log (x)) \log (\frac {e^{679} x-\log (x)}{x})+(e^{679} x \log (2)-\log (2) \log (x)) \log ^2(\frac {e^{679} x-\log (x)}{x})}{-e^{679} x+\log (x)} \, dx\)

Optimal. Leaf size=24 \[ -3+x \log (2) \left (x-\log ^2\left (e^{679}-\frac {\log (x)}{x}\right )\right ) \]

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Rubi [F]  time = 0.41, 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 {-2 e^{679} x^2 \log (2)+2 x \log (2) \log (x)+(-2 \log (2)+2 \log (2) \log (x)) \log \left (\frac {e^{679} x-\log (x)}{x}\right )+\left (e^{679} x \log (2)-\log (2) \log (x)\right ) \log ^2\left (\frac {e^{679} x-\log (x)}{x}\right )}{-e^{679} x+\log (x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-2*E^679*x^2*Log[2] + 2*x*Log[2]*Log[x] + (-2*Log[2] + 2*Log[2]*Log[x])*Log[(E^679*x - Log[x])/x] + (E^67
9*x*Log[2] - Log[2]*Log[x])*Log[(E^679*x - Log[x])/x]^2)/(-(E^679*x) + Log[x]),x]

[Out]

(x^2*Log[4])/2 + 2*Log[2]*Defer[Int][Log[E^679 - Log[x]/x]/(E^679*x - Log[x]), x] - 2*Log[2]*Defer[Int][(Log[x
]*Log[E^679 - Log[x]/x])/(E^679*x - Log[x]), x] - Log[2]*Defer[Int][Log[E^679 - Log[x]/x]^2, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (x \log (4)-\frac {2 \log (2) (-1+\log (x)) \log \left (e^{679}-\frac {\log (x)}{x}\right )}{e^{679} x-\log (x)}-\log (2) \log ^2\left (e^{679}-\frac {\log (x)}{x}\right )\right ) \, dx\\ &=\frac {1}{2} x^2 \log (4)-\log (2) \int \log ^2\left (e^{679}-\frac {\log (x)}{x}\right ) \, dx-(2 \log (2)) \int \frac {(-1+\log (x)) \log \left (e^{679}-\frac {\log (x)}{x}\right )}{e^{679} x-\log (x)} \, dx\\ &=\frac {1}{2} x^2 \log (4)-\log (2) \int \log ^2\left (e^{679}-\frac {\log (x)}{x}\right ) \, dx-(2 \log (2)) \int \left (-\frac {\log \left (e^{679}-\frac {\log (x)}{x}\right )}{e^{679} x-\log (x)}+\frac {\log (x) \log \left (e^{679}-\frac {\log (x)}{x}\right )}{e^{679} x-\log (x)}\right ) \, dx\\ &=\frac {1}{2} x^2 \log (4)-\log (2) \int \log ^2\left (e^{679}-\frac {\log (x)}{x}\right ) \, dx+(2 \log (2)) \int \frac {\log \left (e^{679}-\frac {\log (x)}{x}\right )}{e^{679} x-\log (x)} \, dx-(2 \log (2)) \int \frac {\log (x) \log \left (e^{679}-\frac {\log (x)}{x}\right )}{e^{679} x-\log (x)} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [F]  time = 1.53, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {-2 e^{679} x^2 \log (2)+2 x \log (2) \log (x)+(-2 \log (2)+2 \log (2) \log (x)) \log \left (\frac {e^{679} x-\log (x)}{x}\right )+\left (e^{679} x \log (2)-\log (2) \log (x)\right ) \log ^2\left (\frac {e^{679} x-\log (x)}{x}\right )}{-e^{679} x+\log (x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[(-2*E^679*x^2*Log[2] + 2*x*Log[2]*Log[x] + (-2*Log[2] + 2*Log[2]*Log[x])*Log[(E^679*x - Log[x])/x] +
(E^679*x*Log[2] - Log[2]*Log[x])*Log[(E^679*x - Log[x])/x]^2)/(-(E^679*x) + Log[x]),x]

[Out]

Integrate[(-2*E^679*x^2*Log[2] + 2*x*Log[2]*Log[x] + (-2*Log[2] + 2*Log[2]*Log[x])*Log[(E^679*x - Log[x])/x] +
(E^679*x*Log[2] - Log[2]*Log[x])*Log[(E^679*x - Log[x])/x]^2)/(-(E^679*x) + Log[x]), x]

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fricas [A]  time = 0.91, size = 28, normalized size = 1.17 \begin {gather*} -x \log \relax (2) \log \left (\frac {x e^{679} - \log \relax (x)}{x}\right )^{2} + x^{2} \log \relax (2) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-log(2)*log(x)+x*exp(679)*log(2))*log((-log(x)+x*exp(679))/x)^2+(2*log(2)*log(x)-2*log(2))*log((-l
og(x)+x*exp(679))/x)+2*x*log(2)*log(x)-2*x^2*exp(679)*log(2))/(log(x)-x*exp(679)),x, algorithm="fricas")

[Out]

-x*log(2)*log((x*e^679 - log(x))/x)^2 + x^2*log(2)

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giac [B]  time = 0.23, size = 50, normalized size = 2.08 \begin {gather*} -x \log \relax (2) \log \left (x e^{679} - \log \relax (x)\right )^{2} + 2 \, x \log \relax (2) \log \left (x e^{679} - \log \relax (x)\right ) \log \relax (x) - x \log \relax (2) \log \relax (x)^{2} + x^{2} \log \relax (2) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-log(2)*log(x)+x*exp(679)*log(2))*log((-log(x)+x*exp(679))/x)^2+(2*log(2)*log(x)-2*log(2))*log((-l
og(x)+x*exp(679))/x)+2*x*log(2)*log(x)-2*x^2*exp(679)*log(2))/(log(x)-x*exp(679)),x, algorithm="giac")

[Out]

-x*log(2)*log(x*e^679 - log(x))^2 + 2*x*log(2)*log(x*e^679 - log(x))*log(x) - x*log(2)*log(x)^2 + x^2*log(2)

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maple [C]  time = 0.20, size = 676, normalized size = 28.17

method	result	size
risch	\(-\ln \relax (2) x \ln \left (-\ln \relax (x )+x \,{\mathrm e}^{679}\right )^{2}+\left (i \pi \ln \relax (2) x \,\mathrm {csgn}\left (\frac {i}{x}\right ) \mathrm {csgn}\left (i \left (\ln \relax (x )-x \,{\mathrm e}^{679}\right )\right ) \mathrm {csgn}\left (\frac {i \left (\ln \relax (x )-x \,{\mathrm e}^{679}\right )}{x}\right )-i \pi \ln \relax (2) x \,\mathrm {csgn}\left (\frac {i}{x}\right ) \mathrm {csgn}\left (\frac {i \left (\ln \relax (x )-x \,{\mathrm e}^{679}\right )}{x}\right )^{2}+i \pi \ln \relax (2) x \,\mathrm {csgn}\left (i \left (\ln \relax (x )-x \,{\mathrm e}^{679}\right )\right ) \mathrm {csgn}\left (\frac {i \left (\ln \relax (x )-x \,{\mathrm e}^{679}\right )}{x}\right )^{2}-i \pi \ln \relax (2) x \mathrm {csgn}\left (\frac {i \left (\ln \relax (x )-x \,{\mathrm e}^{679}\right )}{x}\right )^{3}+2 x \ln \relax (2) \ln \relax (x )\right ) \ln \left (-\ln \relax (x )+x \,{\mathrm e}^{679}\right )-\ln \relax (2) x \ln \relax (x )^{2}+i \pi \ln \relax (2) x \mathrm {csgn}\left (\frac {i \left (\ln \relax (x )-x \,{\mathrm e}^{679}\right )}{x}\right )^{3} \ln \relax (x )-i \pi \ln \relax (2) x \,\mathrm {csgn}\left (i \left (\ln \relax (x )-x \,{\mathrm e}^{679}\right )\right ) \mathrm {csgn}\left (\frac {i \left (\ln \relax (x )-x \,{\mathrm e}^{679}\right )}{x}\right )^{2} \ln \relax (x )-i \pi \ln \relax (2) x \,\mathrm {csgn}\left (\frac {i}{x}\right ) \mathrm {csgn}\left (i \left (\ln \relax (x )-x \,{\mathrm e}^{679}\right )\right ) \mathrm {csgn}\left (\frac {i \left (\ln \relax (x )-x \,{\mathrm e}^{679}\right )}{x}\right ) \ln \relax (x )+i \pi \ln \relax (2) x \,\mathrm {csgn}\left (\frac {i}{x}\right ) \mathrm {csgn}\left (\frac {i \left (\ln \relax (x )-x \,{\mathrm e}^{679}\right )}{x}\right )^{2} \ln \relax (x )+\frac {\pi ^{2} \ln \relax (2) x \mathrm {csgn}\left (\frac {i}{x}\right )^{2} \mathrm {csgn}\left (i \left (\ln \relax (x )-x \,{\mathrm e}^{679}\right )\right )^{2} \mathrm {csgn}\left (\frac {i \left (\ln \relax (x )-x \,{\mathrm e}^{679}\right )}{x}\right )^{2}}{4}-\frac {\pi ^{2} \ln \relax (2) x \mathrm {csgn}\left (\frac {i}{x}\right )^{2} \mathrm {csgn}\left (i \left (\ln \relax (x )-x \,{\mathrm e}^{679}\right )\right ) \mathrm {csgn}\left (\frac {i \left (\ln \relax (x )-x \,{\mathrm e}^{679}\right )}{x}\right )^{3}}{2}+\frac {\pi ^{2} \ln \relax (2) x \mathrm {csgn}\left (\frac {i}{x}\right )^{2} \mathrm {csgn}\left (\frac {i \left (\ln \relax (x )-x \,{\mathrm e}^{679}\right )}{x}\right )^{4}}{4}+\frac {\pi ^{2} \ln \relax (2) x \,\mathrm {csgn}\left (\frac {i}{x}\right ) \mathrm {csgn}\left (i \left (\ln \relax (x )-x \,{\mathrm e}^{679}\right )\right )^{2} \mathrm {csgn}\left (\frac {i \left (\ln \relax (x )-x \,{\mathrm e}^{679}\right )}{x}\right )^{3}}{2}-\pi ^{2} \ln \relax (2) x \,\mathrm {csgn}\left (\frac {i}{x}\right ) \mathrm {csgn}\left (i \left (\ln \relax (x )-x \,{\mathrm e}^{679}\right )\right ) \mathrm {csgn}\left (\frac {i \left (\ln \relax (x )-x \,{\mathrm e}^{679}\right )}{x}\right )^{4}+\frac {\pi ^{2} \ln \relax (2) x \,\mathrm {csgn}\left (\frac {i}{x}\right ) \mathrm {csgn}\left (\frac {i \left (\ln \relax (x )-x \,{\mathrm e}^{679}\right )}{x}\right )^{5}}{2}+\frac {\pi ^{2} \ln \relax (2) x \mathrm {csgn}\left (i \left (\ln \relax (x )-x \,{\mathrm e}^{679}\right )\right )^{2} \mathrm {csgn}\left (\frac {i \left (\ln \relax (x )-x \,{\mathrm e}^{679}\right )}{x}\right )^{4}}{4}-\frac {\pi ^{2} \ln \relax (2) x \,\mathrm {csgn}\left (i \left (\ln \relax (x )-x \,{\mathrm e}^{679}\right )\right ) \mathrm {csgn}\left (\frac {i \left (\ln \relax (x )-x \,{\mathrm e}^{679}\right )}{x}\right )^{5}}{2}+\frac {\pi ^{2} \ln \relax (2) x \mathrm {csgn}\left (\frac {i \left (\ln \relax (x )-x \,{\mathrm e}^{679}\right )}{x}\right )^{6}}{4}+x^{2} \ln \relax (2)\)	\(676\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-ln(2)*ln(x)+x*exp(679)*ln(2))*ln((-ln(x)+x*exp(679))/x)^2+(2*ln(2)*ln(x)-2*ln(2))*ln((-ln(x)+x*exp(679)
)/x)+2*x*ln(2)*ln(x)-2*x^2*exp(679)*ln(2))/(ln(x)-x*exp(679)),x,method=_RETURNVERBOSE)

[Out]

-ln(2)*x*ln(-ln(x)+x*exp(679))^2+(I*Pi*ln(2)*x*csgn(I/x)*csgn(I*(ln(x)-x*exp(679)))*csgn(I*(ln(x)-x*exp(679))/
x)-I*Pi*ln(2)*x*csgn(I/x)*csgn(I*(ln(x)-x*exp(679))/x)^2+I*Pi*ln(2)*x*csgn(I*(ln(x)-x*exp(679)))*csgn(I*(ln(x)
-x*exp(679))/x)^2-I*Pi*ln(2)*x*csgn(I*(ln(x)-x*exp(679))/x)^3+2*x*ln(2)*ln(x))*ln(-ln(x)+x*exp(679))-ln(2)*x*l
n(x)^2+I*Pi*ln(2)*x*csgn(I*(ln(x)-x*exp(679))/x)^3*ln(x)-I*Pi*ln(2)*x*csgn(I*(ln(x)-x*exp(679)))*csgn(I*(ln(x)
-x*exp(679))/x)^2*ln(x)-I*Pi*ln(2)*x*csgn(I/x)*csgn(I*(ln(x)-x*exp(679)))*csgn(I*(ln(x)-x*exp(679))/x)*ln(x)+I
*Pi*ln(2)*x*csgn(I/x)*csgn(I*(ln(x)-x*exp(679))/x)^2*ln(x)+1/4*Pi^2*ln(2)*x*csgn(I/x)^2*csgn(I*(ln(x)-x*exp(67
9)))^2*csgn(I*(ln(x)-x*exp(679))/x)^2-1/2*Pi^2*ln(2)*x*csgn(I/x)^2*csgn(I*(ln(x)-x*exp(679)))*csgn(I*(ln(x)-x*
exp(679))/x)^3+1/4*Pi^2*ln(2)*x*csgn(I/x)^2*csgn(I*(ln(x)-x*exp(679))/x)^4+1/2*Pi^2*ln(2)*x*csgn(I/x)*csgn(I*(
ln(x)-x*exp(679)))^2*csgn(I*(ln(x)-x*exp(679))/x)^3-Pi^2*ln(2)*x*csgn(I/x)*csgn(I*(ln(x)-x*exp(679)))*csgn(I*(
ln(x)-x*exp(679))/x)^4+1/2*Pi^2*ln(2)*x*csgn(I/x)*csgn(I*(ln(x)-x*exp(679))/x)^5+1/4*Pi^2*ln(2)*x*csgn(I*(ln(x
)-x*exp(679)))^2*csgn(I*(ln(x)-x*exp(679))/x)^4-1/2*Pi^2*ln(2)*x*csgn(I*(ln(x)-x*exp(679)))*csgn(I*(ln(x)-x*ex
p(679))/x)^5+1/4*Pi^2*ln(2)*x*csgn(I*(ln(x)-x*exp(679))/x)^6+x^2*ln(2)

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maxima [B]  time = 0.49, size = 50, normalized size = 2.08 \begin {gather*} -x \log \relax (2) \log \left (x e^{679} - \log \relax (x)\right )^{2} + 2 \, x \log \relax (2) \log \left (x e^{679} - \log \relax (x)\right ) \log \relax (x) - x \log \relax (2) \log \relax (x)^{2} + x^{2} \log \relax (2) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-log(2)*log(x)+x*exp(679)*log(2))*log((-log(x)+x*exp(679))/x)^2+(2*log(2)*log(x)-2*log(2))*log((-l
og(x)+x*exp(679))/x)+2*x*log(2)*log(x)-2*x^2*exp(679)*log(2))/(log(x)-x*exp(679)),x, algorithm="maxima")

[Out]

-x*log(2)*log(x*e^679 - log(x))^2 + 2*x*log(2)*log(x*e^679 - log(x))*log(x) - x*log(2)*log(x)^2 + x^2*log(2)

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mupad [B]  time = 3.88, size = 24, normalized size = 1.00 \begin {gather*} x\,\ln \relax (2)\,\left (x-{\ln \left (-\frac {\ln \relax (x)-x\,{\mathrm {e}}^{679}}{x}\right )}^2\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(log(-(log(x) - x*exp(679))/x)*(2*log(2) - 2*log(2)*log(x)) + log(-(log(x) - x*exp(679))/x)^2*(log(2)*log
(x) - x*exp(679)*log(2)) + 2*x^2*exp(679)*log(2) - 2*x*log(2)*log(x))/(log(x) - x*exp(679)),x)

[Out]

x*log(2)*(x - log(-(log(x) - x*exp(679))/x)^2)

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sympy [A]  time = 0.45, size = 24, normalized size = 1.00 \begin {gather*} x^{2} \log {\relax (2 )} - x \log {\relax (2 )} \log {\left (\frac {x e^{679} - \log {\relax (x )}}{x} \right )}^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-ln(2)*ln(x)+x*exp(679)*ln(2))*ln((-ln(x)+x*exp(679))/x)**2+(2*ln(2)*ln(x)-2*ln(2))*ln((-ln(x)+x*e
xp(679))/x)+2*x*ln(2)*ln(x)-2*x**2*exp(679)*ln(2))/(ln(x)-x*exp(679)),x)

[Out]

x**2*log(2) - x*log(2)*log((x*exp(679) - log(x))/x)**2

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