3.32.84 \(\int \frac {(960-960 x+300 x^2-30 x^3+e^x (-960+960 x-300 x^2+30 x^3)) \log (-2+x)+(120-60 x+e^x (-120+60 x)) \log ^2(-2+x)+(-480 x+240 x^2-30 x^3+e^x (480 x-240 x^2+30 x^3)+(480 x-360 x^2+60 x^3+e^x (-1440 x+1320 x^2-360 x^3+30 x^4)) \log (-2+x)+e^x (-120 x+60 x^2) \log ^2(-2+x)) \log (x)}{-512 x+768 x^2-448 x^3+128 x^4-18 x^5+x^6+(-128 x+128 x^2-40 x^3+4 x^4) \log (-2+x)+(-8 x+4 x^2) \log ^2(-2+x)} \, dx\)

Optimal. Leaf size=25 \[ \frac {30 \left (-1+e^x\right ) \log (x)}{2+\frac {(-4+x)^2}{\log (-2+x)}} \]

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Rubi [F]  time = 180.00, 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*} \text {\$Aborted} \end {gather*}

Verification is not applicable to the result.

[In]

Int[((960 - 960*x + 300*x^2 - 30*x^3 + E^x*(-960 + 960*x - 300*x^2 + 30*x^3))*Log[-2 + x] + (120 - 60*x + E^x*
(-120 + 60*x))*Log[-2 + x]^2 + (-480*x + 240*x^2 - 30*x^3 + E^x*(480*x - 240*x^2 + 30*x^3) + (480*x - 360*x^2
+ 60*x^3 + E^x*(-1440*x + 1320*x^2 - 360*x^3 + 30*x^4))*Log[-2 + x] + E^x*(-120*x + 60*x^2)*Log[-2 + x]^2)*Log
[x])/(-512*x + 768*x^2 - 448*x^3 + 128*x^4 - 18*x^5 + x^6 + (-128*x + 128*x^2 - 40*x^3 + 4*x^4)*Log[-2 + x] +
(-8*x + 4*x^2)*Log[-2 + x]^2),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [A]  time = 0.15, size = 27, normalized size = 1.08 \begin {gather*} \frac {30 \left (-1+e^x\right ) \log (-2+x) \log (x)}{(-4+x)^2+2 \log (-2+x)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[((960 - 960*x + 300*x^2 - 30*x^3 + E^x*(-960 + 960*x - 300*x^2 + 30*x^3))*Log[-2 + x] + (120 - 60*x
+ E^x*(-120 + 60*x))*Log[-2 + x]^2 + (-480*x + 240*x^2 - 30*x^3 + E^x*(480*x - 240*x^2 + 30*x^3) + (480*x - 36
0*x^2 + 60*x^3 + E^x*(-1440*x + 1320*x^2 - 360*x^3 + 30*x^4))*Log[-2 + x] + E^x*(-120*x + 60*x^2)*Log[-2 + x]^
2)*Log[x])/(-512*x + 768*x^2 - 448*x^3 + 128*x^4 - 18*x^5 + x^6 + (-128*x + 128*x^2 - 40*x^3 + 4*x^4)*Log[-2 +
x] + (-8*x + 4*x^2)*Log[-2 + x]^2),x]

[Out]

(30*(-1 + E^x)*Log[-2 + x]*Log[x])/((-4 + x)^2 + 2*Log[-2 + x])

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fricas [A]  time = 0.70, size = 28, normalized size = 1.12 \begin {gather*} \frac {30 \, {\left (e^{x} - 1\right )} \log \left (x - 2\right ) \log \relax (x)}{x^{2} - 8 \, x + 2 \, \log \left (x - 2\right ) + 16} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((60*x^2-120*x)*exp(x)*log(x-2)^2+((30*x^4-360*x^3+1320*x^2-1440*x)*exp(x)+60*x^3-360*x^2+480*x)*lo
g(x-2)+(30*x^3-240*x^2+480*x)*exp(x)-30*x^3+240*x^2-480*x)*log(x)+((60*x-120)*exp(x)-60*x+120)*log(x-2)^2+((30
*x^3-300*x^2+960*x-960)*exp(x)-30*x^3+300*x^2-960*x+960)*log(x-2))/((4*x^2-8*x)*log(x-2)^2+(4*x^4-40*x^3+128*x
^2-128*x)*log(x-2)+x^6-18*x^5+128*x^4-448*x^3+768*x^2-512*x),x, algorithm="fricas")

[Out]

30*(e^x - 1)*log(x - 2)*log(x)/(x^2 - 8*x + 2*log(x - 2) + 16)

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giac [A]  time = 0.65, size = 36, normalized size = 1.44 \begin {gather*} \frac {30 \, {\left (e^{x} \log \left (x - 2\right ) \log \relax (x) - \log \left (x - 2\right ) \log \relax (x)\right )}}{x^{2} - 8 \, x + 2 \, \log \left (x - 2\right ) + 16} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((60*x^2-120*x)*exp(x)*log(x-2)^2+((30*x^4-360*x^3+1320*x^2-1440*x)*exp(x)+60*x^3-360*x^2+480*x)*lo
g(x-2)+(30*x^3-240*x^2+480*x)*exp(x)-30*x^3+240*x^2-480*x)*log(x)+((60*x-120)*exp(x)-60*x+120)*log(x-2)^2+((30
*x^3-300*x^2+960*x-960)*exp(x)-30*x^3+300*x^2-960*x+960)*log(x-2))/((4*x^2-8*x)*log(x-2)^2+(4*x^4-40*x^3+128*x
^2-128*x)*log(x-2)+x^6-18*x^5+128*x^4-448*x^3+768*x^2-512*x),x, algorithm="giac")

[Out]

30*(e^x*log(x - 2)*log(x) - log(x - 2)*log(x))/(x^2 - 8*x + 2*log(x - 2) + 16)

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maple [B]  time = 0.08, size = 57, normalized size = 2.28

method	result	size
risch	\(15 \,{\mathrm e}^{x} \ln \relax (x )-15 \ln \relax (x )-\frac {15 \left ({\mathrm e}^{x} x^{2}-x^{2}-8 \,{\mathrm e}^{x} x +8 x +16 \,{\mathrm e}^{x}-16\right ) \ln \relax (x )}{x^{2}+2 \ln \left (x -2\right )-8 x +16}\)	\(57\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((60*x^2-120*x)*exp(x)*ln(x-2)^2+((30*x^4-360*x^3+1320*x^2-1440*x)*exp(x)+60*x^3-360*x^2+480*x)*ln(x-2)+(
30*x^3-240*x^2+480*x)*exp(x)-30*x^3+240*x^2-480*x)*ln(x)+((60*x-120)*exp(x)-60*x+120)*ln(x-2)^2+((30*x^3-300*x
^2+960*x-960)*exp(x)-30*x^3+300*x^2-960*x+960)*ln(x-2))/((4*x^2-8*x)*ln(x-2)^2+(4*x^4-40*x^3+128*x^2-128*x)*ln
(x-2)+x^6-18*x^5+128*x^4-448*x^3+768*x^2-512*x),x,method=_RETURNVERBOSE)

[Out]

15*exp(x)*ln(x)-15*ln(x)-15*(exp(x)*x^2-x^2-8*exp(x)*x+8*x+16*exp(x)-16)*ln(x)/(x^2+2*ln(x-2)-8*x+16)

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maxima [A]  time = 0.53, size = 45, normalized size = 1.80 \begin {gather*} \frac {15 \, {\left (2 \, e^{x} \log \left (x - 2\right ) \log \relax (x) + {\left (x^{2} - 8 \, x + 16\right )} \log \relax (x)\right )}}{x^{2} - 8 \, x + 2 \, \log \left (x - 2\right ) + 16} - 15 \, \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((60*x^2-120*x)*exp(x)*log(x-2)^2+((30*x^4-360*x^3+1320*x^2-1440*x)*exp(x)+60*x^3-360*x^2+480*x)*lo
g(x-2)+(30*x^3-240*x^2+480*x)*exp(x)-30*x^3+240*x^2-480*x)*log(x)+((60*x-120)*exp(x)-60*x+120)*log(x-2)^2+((30
*x^3-300*x^2+960*x-960)*exp(x)-30*x^3+300*x^2-960*x+960)*log(x-2))/((4*x^2-8*x)*log(x-2)^2+(4*x^4-40*x^3+128*x
^2-128*x)*log(x-2)+x^6-18*x^5+128*x^4-448*x^3+768*x^2-512*x),x, algorithm="maxima")

[Out]

15*(2*e^x*log(x - 2)*log(x) + (x^2 - 8*x + 16)*log(x))/(x^2 - 8*x + 2*log(x - 2) + 16) - 15*log(x)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int -\frac {\ln \left (x-2\right )\,\left (300\,x^2-960\,x-30\,x^3+{\mathrm {e}}^x\,\left (30\,x^3-300\,x^2+960\,x-960\right )+960\right )-\ln \relax (x)\,\left (480\,x-\ln \left (x-2\right )\,\left (480\,x-{\mathrm {e}}^x\,\left (-30\,x^4+360\,x^3-1320\,x^2+1440\,x\right )-360\,x^2+60\,x^3\right )-240\,x^2+30\,x^3-{\mathrm {e}}^x\,\left (30\,x^3-240\,x^2+480\,x\right )+{\ln \left (x-2\right )}^2\,{\mathrm {e}}^x\,\left (120\,x-60\,x^2\right )\right )+{\ln \left (x-2\right )}^2\,\left ({\mathrm {e}}^x\,\left (60\,x-120\right )-60\,x+120\right )}{512\,x+{\ln \left (x-2\right )}^2\,\left (8\,x-4\,x^2\right )+\ln \left (x-2\right )\,\left (-4\,x^4+40\,x^3-128\,x^2+128\,x\right )-768\,x^2+448\,x^3-128\,x^4+18\,x^5-x^6} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(log(x - 2)*(300*x^2 - 960*x - 30*x^3 + exp(x)*(960*x - 300*x^2 + 30*x^3 - 960) + 960) - log(x)*(480*x -
log(x - 2)*(480*x - exp(x)*(1440*x - 1320*x^2 + 360*x^3 - 30*x^4) - 360*x^2 + 60*x^3) - 240*x^2 + 30*x^3 - exp
(x)*(480*x - 240*x^2 + 30*x^3) + log(x - 2)^2*exp(x)*(120*x - 60*x^2)) + log(x - 2)^2*(exp(x)*(60*x - 120) - 6
0*x + 120))/(512*x + log(x - 2)^2*(8*x - 4*x^2) + log(x - 2)*(128*x - 128*x^2 + 40*x^3 - 4*x^4) - 768*x^2 + 44
8*x^3 - 128*x^4 + 18*x^5 - x^6),x)

[Out]

int(-(log(x - 2)*(300*x^2 - 960*x - 30*x^3 + exp(x)*(960*x - 300*x^2 + 30*x^3 - 960) + 960) - log(x)*(480*x -
log(x - 2)*(480*x - exp(x)*(1440*x - 1320*x^2 + 360*x^3 - 30*x^4) - 360*x^2 + 60*x^3) - 240*x^2 + 30*x^3 - exp
(x)*(480*x - 240*x^2 + 30*x^3) + log(x - 2)^2*exp(x)*(120*x - 60*x^2)) + log(x - 2)^2*(exp(x)*(60*x - 120) - 6
0*x + 120))/(512*x + log(x - 2)^2*(8*x - 4*x^2) + log(x - 2)*(128*x - 128*x^2 + 40*x^3 - 4*x^4) - 768*x^2 + 44
8*x^3 - 128*x^4 + 18*x^5 - x^6), x)

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sympy [B]  time = 0.64, size = 68, normalized size = 2.72 \begin {gather*} \frac {15 x^{2} \log {\relax (x )} - 120 x \log {\relax (x )} + 240 \log {\relax (x )}}{x^{2} - 8 x + 2 \log {\left (x - 2 \right )} + 16} - 15 \log {\relax (x )} + \frac {30 e^{x} \log {\relax (x )} \log {\left (x - 2 \right )}}{x^{2} - 8 x + 2 \log {\left (x - 2 \right )} + 16} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((60*x**2-120*x)*exp(x)*ln(x-2)**2+((30*x**4-360*x**3+1320*x**2-1440*x)*exp(x)+60*x**3-360*x**2+480
*x)*ln(x-2)+(30*x**3-240*x**2+480*x)*exp(x)-30*x**3+240*x**2-480*x)*ln(x)+((60*x-120)*exp(x)-60*x+120)*ln(x-2)
**2+((30*x**3-300*x**2+960*x-960)*exp(x)-30*x**3+300*x**2-960*x+960)*ln(x-2))/((4*x**2-8*x)*ln(x-2)**2+(4*x**4
-40*x**3+128*x**2-128*x)*ln(x-2)+x**6-18*x**5+128*x**4-448*x**3+768*x**2-512*x),x)

[Out]

(15*x**2*log(x) - 120*x*log(x) + 240*log(x))/(x**2 - 8*x + 2*log(x - 2) + 16) - 15*log(x) + 30*exp(x)*log(x)*l
og(x - 2)/(x**2 - 8*x + 2*log(x - 2) + 16)

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