3.35.61 \(\int (-7290 x^{10}+8748 x^{11}+e^{16} (-7290 x^6+5832 x^7)+e^{12} (29160 x^7-26244 x^8)+e^8 (-43740 x^8+43740 x^9)+e^4 (29160 x^9-32076 x^{10})+(36450 x^9-80190 x^{10}+e^{16} (36450 x^5-51030 x^6)+e^{12} (-145800 x^6+233280 x^7)+e^8 (218700 x^7-393660 x^8)+e^4 (-145800 x^8+291600 x^9)) \log (x)+(109350 e^{16} x^5-510300 e^{12} x^6+874800 e^8 x^7-656100 e^4 x^8+182250 x^9) \log ^2(x)) \, dx\)

Optimal. Leaf size=24 \[ 1+729 x^6 \left (-e^4+x\right )^4 (x-5 \log (x))^2 \]

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Rubi [B]  time = 0.38, antiderivative size = 344, normalized size of antiderivative = 14.33, number of steps used = 25, number of rules used = 3, integrand size = 188, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.016, Rules used = {2356, 2304, 2305} \begin {gather*} 729 x^{12}-2916 e^4 x^{11}-7290 x^{11} \log (x)-\frac {729}{2} \left (1+8 e^4\right ) x^{10}+4374 e^8 x^{10}+2916 e^4 x^{10}+\frac {729 x^{10}}{2}+18225 x^{10} \log ^2(x)+3645 \left (1+8 e^4\right ) x^{10} \log (x)-3645 x^{10} \log (x)+180 e^4 \left (10+27 e^4\right ) x^9-2916 e^{12} x^9-4860 e^8 x^9-1800 e^4 x^9-72900 e^4 x^9 \log ^2(x)-1620 e^4 \left (10+27 e^4\right ) x^9 \log (x)+16200 e^4 x^9 \log (x)-\frac {3645}{16} e^8 \left (15+16 e^4\right ) x^8+729 e^{16} x^8+3645 e^{12} x^8+\frac {54675 e^8 x^8}{16}+109350 e^8 x^8 \log ^2(x)+\frac {3645}{2} e^8 \left (15+16 e^4\right ) x^8 \log (x)-\frac {54675}{2} e^8 x^8 \log (x)+\frac {7290}{49} e^{12} \left (20+7 e^4\right ) x^7-\frac {7290 e^{16} x^7}{7}-\frac {145800 e^{12} x^7}{49}-72900 e^{12} x^7 \log ^2(x)-\frac {7290}{7} e^{12} \left (20+7 e^4\right ) x^7 \log (x)+\frac {145800}{7} e^{12} x^7 \log (x)+18225 e^{16} x^6 \log ^2(x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-7290*x^10 + 8748*x^11 + E^16*(-7290*x^6 + 5832*x^7) + E^12*(29160*x^7 - 26244*x^8) + E^8*(-43740*x^8 + 43
740*x^9) + E^4*(29160*x^9 - 32076*x^10) + (36450*x^9 - 80190*x^10 + E^16*(36450*x^5 - 51030*x^6) + E^12*(-1458
00*x^6 + 233280*x^7) + E^8*(218700*x^7 - 393660*x^8) + E^4*(-145800*x^8 + 291600*x^9))*Log[x] + (109350*E^16*x
^5 - 510300*E^12*x^6 + 874800*E^8*x^7 - 656100*E^4*x^8 + 182250*x^9)*Log[x]^2,x]

[Out]

(-145800*E^12*x^7)/49 - (7290*E^16*x^7)/7 + (7290*E^12*(20 + 7*E^4)*x^7)/49 + (54675*E^8*x^8)/16 + 3645*E^12*x
^8 + 729*E^16*x^8 - (3645*E^8*(15 + 16*E^4)*x^8)/16 - 1800*E^4*x^9 - 4860*E^8*x^9 - 2916*E^12*x^9 + 180*E^4*(1
0 + 27*E^4)*x^9 + (729*x^10)/2 + 2916*E^4*x^10 + 4374*E^8*x^10 - (729*(1 + 8*E^4)*x^10)/2 - 2916*E^4*x^11 + 72
9*x^12 + (145800*E^12*x^7*Log[x])/7 - (7290*E^12*(20 + 7*E^4)*x^7*Log[x])/7 - (54675*E^8*x^8*Log[x])/2 + (3645
*E^8*(15 + 16*E^4)*x^8*Log[x])/2 + 16200*E^4*x^9*Log[x] - 1620*E^4*(10 + 27*E^4)*x^9*Log[x] - 3645*x^10*Log[x]
+ 3645*(1 + 8*E^4)*x^10*Log[x] - 7290*x^11*Log[x] + 18225*E^16*x^6*Log[x]^2 - 72900*E^12*x^7*Log[x]^2 + 10935
0*E^8*x^8*Log[x]^2 - 72900*E^4*x^9*Log[x]^2 + 18225*x^10*Log[x]^2

Rule 2304

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))*((d_.)*(x_))^(m_.), x_Symbol] :> Simp[((d*x)^(m + 1)*(a + b*Log[c*x^
n]))/(d*(m + 1)), x] - Simp[(b*n*(d*x)^(m + 1))/(d*(m + 1)^2), x] /; FreeQ[{a, b, c, d, m, n}, x] && NeQ[m, -1
]

Rule 2305

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)*((d_.)*(x_))^(m_.), x_Symbol] :> Simp[((d*x)^(m + 1)*(a + b*Lo
g[c*x^n])^p)/(d*(m + 1)), x] - Dist[(b*n*p)/(m + 1), Int[(d*x)^m*(a + b*Log[c*x^n])^(p - 1), x], x] /; FreeQ[{
a, b, c, d, m, n}, x] && NeQ[m, -1] && GtQ[p, 0]

Rule 2356

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)*(Polyx_), x_Symbol] :> Int[ExpandIntegrand[Polyx*(a + b*Log[c*
x^n])^p, x], x] /; FreeQ[{a, b, c, n, p}, x] && PolynomialQ[Polyx, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-\frac {7290 x^{11}}{11}+729 x^{12}+e^4 \int \left (29160 x^9-32076 x^{10}\right ) \, dx+e^8 \int \left (-43740 x^8+43740 x^9\right ) \, dx+e^{12} \int \left (29160 x^7-26244 x^8\right ) \, dx+e^{16} \int \left (-7290 x^6+5832 x^7\right ) \, dx+\int \left (36450 x^9-80190 x^{10}+e^{16} \left (36450 x^5-51030 x^6\right )+e^{12} \left (-145800 x^6+233280 x^7\right )+e^8 \left (218700 x^7-393660 x^8\right )+e^4 \left (-145800 x^8+291600 x^9\right )\right ) \log (x) \, dx+\int \left (109350 e^{16} x^5-510300 e^{12} x^6+874800 e^8 x^7-656100 e^4 x^8+182250 x^9\right ) \log ^2(x) \, dx\\ &=-\frac {7290}{7} e^{16} x^7+3645 e^{12} x^8+729 e^{16} x^8-4860 e^8 x^9-2916 e^{12} x^9+2916 e^4 x^{10}+4374 e^8 x^{10}-\frac {7290 x^{11}}{11}-2916 e^4 x^{11}+729 x^{12}+\int \left (36450 e^{16} x^5 \log (x)-7290 e^{12} \left (20+7 e^4\right ) x^6 \log (x)+14580 e^8 \left (15+16 e^4\right ) x^7 \log (x)-14580 e^4 \left (10+27 e^4\right ) x^8 \log (x)+36450 \left (1+8 e^4\right ) x^9 \log (x)-80190 x^{10} \log (x)\right ) \, dx+\int \left (109350 e^{16} x^5 \log ^2(x)-510300 e^{12} x^6 \log ^2(x)+874800 e^8 x^7 \log ^2(x)-656100 e^4 x^8 \log ^2(x)+182250 x^9 \log ^2(x)\right ) \, dx\\ &=-\frac {7290}{7} e^{16} x^7+3645 e^{12} x^8+729 e^{16} x^8-4860 e^8 x^9-2916 e^{12} x^9+2916 e^4 x^{10}+4374 e^8 x^{10}-\frac {7290 x^{11}}{11}-2916 e^4 x^{11}+729 x^{12}-80190 \int x^{10} \log (x) \, dx+182250 \int x^9 \log ^2(x) \, dx-\left (656100 e^4\right ) \int x^8 \log ^2(x) \, dx+\left (874800 e^8\right ) \int x^7 \log ^2(x) \, dx-\left (510300 e^{12}\right ) \int x^6 \log ^2(x) \, dx+\left (36450 e^{16}\right ) \int x^5 \log (x) \, dx+\left (109350 e^{16}\right ) \int x^5 \log ^2(x) \, dx-\left (7290 e^{12} \left (20+7 e^4\right )\right ) \int x^6 \log (x) \, dx+\left (36450 \left (1+8 e^4\right )\right ) \int x^9 \log (x) \, dx+\left (14580 e^8 \left (15+16 e^4\right )\right ) \int x^7 \log (x) \, dx-\left (14580 e^4 \left (10+27 e^4\right )\right ) \int x^8 \log (x) \, dx\\ &=-\frac {2025}{2} e^{16} x^6-\frac {7290 e^{16} x^7}{7}+\frac {7290}{49} e^{12} \left (20+7 e^4\right ) x^7+3645 e^{12} x^8+729 e^{16} x^8-\frac {3645}{16} e^8 \left (15+16 e^4\right ) x^8-4860 e^8 x^9-2916 e^{12} x^9+180 e^4 \left (10+27 e^4\right ) x^9+2916 e^4 x^{10}+4374 e^8 x^{10}-\frac {729}{2} \left (1+8 e^4\right ) x^{10}-2916 e^4 x^{11}+729 x^{12}+6075 e^{16} x^6 \log (x)-\frac {7290}{7} e^{12} \left (20+7 e^4\right ) x^7 \log (x)+\frac {3645}{2} e^8 \left (15+16 e^4\right ) x^8 \log (x)-1620 e^4 \left (10+27 e^4\right ) x^9 \log (x)+3645 \left (1+8 e^4\right ) x^{10} \log (x)-7290 x^{11} \log (x)+18225 e^{16} x^6 \log ^2(x)-72900 e^{12} x^7 \log ^2(x)+109350 e^8 x^8 \log ^2(x)-72900 e^4 x^9 \log ^2(x)+18225 x^{10} \log ^2(x)-36450 \int x^9 \log (x) \, dx+\left (145800 e^4\right ) \int x^8 \log (x) \, dx-\left (218700 e^8\right ) \int x^7 \log (x) \, dx+\left (145800 e^{12}\right ) \int x^6 \log (x) \, dx-\left (36450 e^{16}\right ) \int x^5 \log (x) \, dx\\ &=-\frac {145800}{49} e^{12} x^7-\frac {7290 e^{16} x^7}{7}+\frac {7290}{49} e^{12} \left (20+7 e^4\right ) x^7+\frac {54675 e^8 x^8}{16}+3645 e^{12} x^8+729 e^{16} x^8-\frac {3645}{16} e^8 \left (15+16 e^4\right ) x^8-1800 e^4 x^9-4860 e^8 x^9-2916 e^{12} x^9+180 e^4 \left (10+27 e^4\right ) x^9+\frac {729 x^{10}}{2}+2916 e^4 x^{10}+4374 e^8 x^{10}-\frac {729}{2} \left (1+8 e^4\right ) x^{10}-2916 e^4 x^{11}+729 x^{12}+\frac {145800}{7} e^{12} x^7 \log (x)-\frac {7290}{7} e^{12} \left (20+7 e^4\right ) x^7 \log (x)-\frac {54675}{2} e^8 x^8 \log (x)+\frac {3645}{2} e^8 \left (15+16 e^4\right ) x^8 \log (x)+16200 e^4 x^9 \log (x)-1620 e^4 \left (10+27 e^4\right ) x^9 \log (x)-3645 x^{10} \log (x)+3645 \left (1+8 e^4\right ) x^{10} \log (x)-7290 x^{11} \log (x)+18225 e^{16} x^6 \log ^2(x)-72900 e^{12} x^7 \log ^2(x)+109350 e^8 x^8 \log ^2(x)-72900 e^4 x^9 \log ^2(x)+18225 x^{10} \log ^2(x)\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.36, size = 152, normalized size = 6.33 \begin {gather*} 1458 \left (\frac {e^{16} x^8}{2}-2 e^{12} x^9+3 e^8 x^{10}-2 e^4 x^{11}+\frac {x^{12}}{2}-5 e^{16} x^7 \log (x)+20 e^{12} x^8 \log (x)-30 e^8 x^9 \log (x)+20 e^4 x^{10} \log (x)-5 x^{11} \log (x)+\frac {25}{2} e^{16} x^6 \log ^2(x)-50 e^{12} x^7 \log ^2(x)+75 e^8 x^8 \log ^2(x)-50 e^4 x^9 \log ^2(x)+\frac {25}{2} x^{10} \log ^2(x)\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-7290*x^10 + 8748*x^11 + E^16*(-7290*x^6 + 5832*x^7) + E^12*(29160*x^7 - 26244*x^8) + E^8*(-43740*x^
8 + 43740*x^9) + E^4*(29160*x^9 - 32076*x^10) + (36450*x^9 - 80190*x^10 + E^16*(36450*x^5 - 51030*x^6) + E^12*
(-145800*x^6 + 233280*x^7) + E^8*(218700*x^7 - 393660*x^8) + E^4*(-145800*x^8 + 291600*x^9))*Log[x] + (109350*
E^16*x^5 - 510300*E^12*x^6 + 874800*E^8*x^7 - 656100*E^4*x^8 + 182250*x^9)*Log[x]^2,x]

[Out]

1458*((E^16*x^8)/2 - 2*E^12*x^9 + 3*E^8*x^10 - 2*E^4*x^11 + x^12/2 - 5*E^16*x^7*Log[x] + 20*E^12*x^8*Log[x] -
30*E^8*x^9*Log[x] + 20*E^4*x^10*Log[x] - 5*x^11*Log[x] + (25*E^16*x^6*Log[x]^2)/2 - 50*E^12*x^7*Log[x]^2 + 75*
E^8*x^8*Log[x]^2 - 50*E^4*x^9*Log[x]^2 + (25*x^10*Log[x]^2)/2)

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fricas [B]  time = 0.78, size = 106, normalized size = 4.42 \begin {gather*} 729 \, x^{12} - 2916 \, x^{11} e^{4} + 4374 \, x^{10} e^{8} - 2916 \, x^{9} e^{12} + 729 \, x^{8} e^{16} + 18225 \, {\left (x^{10} - 4 \, x^{9} e^{4} + 6 \, x^{8} e^{8} - 4 \, x^{7} e^{12} + x^{6} e^{16}\right )} \log \relax (x)^{2} - 7290 \, {\left (x^{11} - 4 \, x^{10} e^{4} + 6 \, x^{9} e^{8} - 4 \, x^{8} e^{12} + x^{7} e^{16}\right )} \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((109350*x^5*exp(4)^4-510300*x^6*exp(4)^3+874800*x^7*exp(4)^2-656100*x^8*exp(4)+182250*x^9)*log(x)^2+
((-51030*x^6+36450*x^5)*exp(4)^4+(233280*x^7-145800*x^6)*exp(4)^3+(-393660*x^8+218700*x^7)*exp(4)^2+(291600*x^
9-145800*x^8)*exp(4)-80190*x^10+36450*x^9)*log(x)+(5832*x^7-7290*x^6)*exp(4)^4+(-26244*x^8+29160*x^7)*exp(4)^3
+(43740*x^9-43740*x^8)*exp(4)^2+(-32076*x^10+29160*x^9)*exp(4)+8748*x^11-7290*x^10,x, algorithm="fricas")

[Out]

729*x^12 - 2916*x^11*e^4 + 4374*x^10*e^8 - 2916*x^9*e^12 + 729*x^8*e^16 + 18225*(x^10 - 4*x^9*e^4 + 6*x^8*e^8
- 4*x^7*e^12 + x^6*e^16)*log(x)^2 - 7290*(x^11 - 4*x^10*e^4 + 6*x^9*e^8 - 4*x^8*e^12 + x^7*e^16)*log(x)

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giac [B]  time = 0.24, size = 188, normalized size = 7.83 \begin {gather*} 729 \, x^{12} - 7290 \, x^{11} \log \relax (x) + 29160 \, x^{10} e^{4} \log \relax (x) + 18225 \, x^{10} \log \relax (x)^{2} - 72900 \, x^{9} e^{4} \log \relax (x)^{2} - 2916 \, x^{10} e^{4} - 43740 \, x^{9} e^{8} \log \relax (x) + 109350 \, x^{8} e^{8} \log \relax (x)^{2} + 4860 \, x^{9} e^{8} + 29160 \, x^{8} e^{12} \log \relax (x) - 72900 \, x^{7} e^{12} \log \relax (x)^{2} - 3645 \, x^{8} e^{12} - 7290 \, x^{7} e^{16} \log \relax (x) + 18225 \, x^{6} e^{16} \log \relax (x)^{2} + \frac {7290}{7} \, x^{7} e^{16} + \frac {729}{7} \, {\left (7 \, x^{8} - 10 \, x^{7}\right )} e^{16} - 729 \, {\left (4 \, x^{9} - 5 \, x^{8}\right )} e^{12} + 486 \, {\left (9 \, x^{10} - 10 \, x^{9}\right )} e^{8} - 2916 \, {\left (x^{11} - x^{10}\right )} e^{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((109350*x^5*exp(4)^4-510300*x^6*exp(4)^3+874800*x^7*exp(4)^2-656100*x^8*exp(4)+182250*x^9)*log(x)^2+
((-51030*x^6+36450*x^5)*exp(4)^4+(233280*x^7-145800*x^6)*exp(4)^3+(-393660*x^8+218700*x^7)*exp(4)^2+(291600*x^
9-145800*x^8)*exp(4)-80190*x^10+36450*x^9)*log(x)+(5832*x^7-7290*x^6)*exp(4)^4+(-26244*x^8+29160*x^7)*exp(4)^3
+(43740*x^9-43740*x^8)*exp(4)^2+(-32076*x^10+29160*x^9)*exp(4)+8748*x^11-7290*x^10,x, algorithm="giac")

[Out]

729*x^12 - 7290*x^11*log(x) + 29160*x^10*e^4*log(x) + 18225*x^10*log(x)^2 - 72900*x^9*e^4*log(x)^2 - 2916*x^10
*e^4 - 43740*x^9*e^8*log(x) + 109350*x^8*e^8*log(x)^2 + 4860*x^9*e^8 + 29160*x^8*e^12*log(x) - 72900*x^7*e^12*
log(x)^2 - 3645*x^8*e^12 - 7290*x^7*e^16*log(x) + 18225*x^6*e^16*log(x)^2 + 7290/7*x^7*e^16 + 729/7*(7*x^8 - 1
0*x^7)*e^16 - 729*(4*x^9 - 5*x^8)*e^12 + 486*(9*x^10 - 10*x^9)*e^8 - 2916*(x^11 - x^10)*e^4

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maple [B]  time = 0.04, size = 131, normalized size = 5.46

method	result	size
risch	\(18225 \,{\mathrm e}^{16} x^{6} \ln \relax (x )^{2}-72900 \,{\mathrm e}^{12} x^{7} \ln \relax (x )^{2}+109350 \,{\mathrm e}^{8} x^{8} \ln \relax (x )^{2}-72900 \,{\mathrm e}^{4} x^{9} \ln \relax (x )^{2}+18225 x^{10} \ln \relax (x )^{2}-7290 \,{\mathrm e}^{16} x^{7} \ln \relax (x )+29160 \,{\mathrm e}^{12} x^{8} \ln \relax (x )-43740 \,{\mathrm e}^{8} x^{9} \ln \relax (x )+29160 \,{\mathrm e}^{4} x^{10} \ln \relax (x )-7290 x^{11} \ln \relax (x )+729 x^{8} {\mathrm e}^{16}-2916 \,{\mathrm e}^{12} x^{9}+4374 \,{\mathrm e}^{8} x^{10}-2916 \,{\mathrm e}^{4} x^{11}+729 x^{12}\)	\(131\)
default	\(18225 x^{10} \ln \relax (x )^{2}-7290 x^{11} \ln \relax (x )+\frac {7290 \,{\mathrm e}^{16} x^{7}}{7}-3645 \,{\mathrm e}^{12} x^{8}+4860 \,{\mathrm e}^{8} x^{9}-2916 \,{\mathrm e}^{4} x^{10}-7290 \,{\mathrm e}^{16} x^{7} \ln \relax (x )+29160 \,{\mathrm e}^{12} x^{8} \ln \relax (x )-43740 \,{\mathrm e}^{8} x^{9} \ln \relax (x )+29160 \,{\mathrm e}^{4} x^{10} \ln \relax (x )+18225 \,{\mathrm e}^{16} x^{6} \ln \relax (x )^{2}-72900 \,{\mathrm e}^{12} x^{7} \ln \relax (x )^{2}+109350 \,{\mathrm e}^{8} x^{8} \ln \relax (x )^{2}-72900 \,{\mathrm e}^{4} x^{9} \ln \relax (x )^{2}+{\mathrm e}^{16} \left (729 x^{8}-\frac {7290}{7} x^{7}\right )+{\mathrm e}^{12} \left (-2916 x^{9}+3645 x^{8}\right )+{\mathrm e}^{8} \left (4374 x^{10}-4860 x^{9}\right )+{\mathrm e}^{4} \left (-2916 x^{11}+2916 x^{10}\right )+729 x^{12}\)	\(211\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((109350*x^5*exp(4)^4-510300*x^6*exp(4)^3+874800*x^7*exp(4)^2-656100*x^8*exp(4)+182250*x^9)*ln(x)^2+((-5103
0*x^6+36450*x^5)*exp(4)^4+(233280*x^7-145800*x^6)*exp(4)^3+(-393660*x^8+218700*x^7)*exp(4)^2+(291600*x^9-14580
0*x^8)*exp(4)-80190*x^10+36450*x^9)*ln(x)+(5832*x^7-7290*x^6)*exp(4)^4+(-26244*x^8+29160*x^7)*exp(4)^3+(43740*
x^9-43740*x^8)*exp(4)^2+(-32076*x^10+29160*x^9)*exp(4)+8748*x^11-7290*x^10,x,method=_RETURNVERBOSE)

[Out]

18225*exp(16)*x^6*ln(x)^2-72900*exp(12)*x^7*ln(x)^2+109350*exp(8)*x^8*ln(x)^2-72900*exp(4)*x^9*ln(x)^2+18225*x
^10*ln(x)^2-7290*exp(16)*x^7*ln(x)+29160*exp(12)*x^8*ln(x)-43740*exp(8)*x^9*ln(x)+29160*exp(4)*x^10*ln(x)-7290
*x^11*ln(x)+729*x^8*exp(16)-2916*exp(12)*x^9+4374*exp(8)*x^10-2916*exp(4)*x^11+729*x^12

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maxima [B]  time = 0.39, size = 308, normalized size = 12.83 \begin {gather*} 729 \, x^{12} + \frac {729}{2} \, {\left (50 \, \log \relax (x)^{2} - 10 \, \log \relax (x) + 1\right )} x^{10} - \frac {729}{2} \, x^{10} {\left (8 \, e^{4} + 1\right )} - 900 \, {\left (81 \, e^{4} \log \relax (x)^{2} - 18 \, e^{4} \log \relax (x) + 2 \, e^{4}\right )} x^{9} + 180 \, x^{9} {\left (27 \, e^{8} + 10 \, e^{4}\right )} + \frac {54675}{16} \, {\left (32 \, e^{8} \log \relax (x)^{2} - 8 \, e^{8} \log \relax (x) + e^{8}\right )} x^{8} - \frac {3645}{16} \, x^{8} {\left (16 \, e^{12} + 15 \, e^{8}\right )} - \frac {72900}{49} \, {\left (49 \, e^{12} \log \relax (x)^{2} - 14 \, e^{12} \log \relax (x) + 2 \, e^{12}\right )} x^{7} + \frac {7290}{49} \, x^{7} {\left (7 \, e^{16} + 20 \, e^{12}\right )} + \frac {2025}{2} \, {\left (18 \, e^{16} \log \relax (x)^{2} - 6 \, e^{16} \log \relax (x) + e^{16}\right )} x^{6} - \frac {2025}{2} \, x^{6} e^{16} + \frac {729}{7} \, {\left (7 \, x^{8} - 10 \, x^{7}\right )} e^{16} - 729 \, {\left (4 \, x^{9} - 5 \, x^{8}\right )} e^{12} + 486 \, {\left (9 \, x^{10} - 10 \, x^{9}\right )} e^{8} - 2916 \, {\left (x^{11} - x^{10}\right )} e^{4} - \frac {405}{14} \, {\left (252 \, x^{11} - 126 \, x^{10} + 42 \, {\left (6 \, x^{7} - 5 \, x^{6}\right )} e^{16} - 144 \, {\left (7 \, x^{8} - 5 \, x^{7}\right )} e^{12} + 189 \, {\left (8 \, x^{9} - 5 \, x^{8}\right )} e^{8} - 112 \, {\left (9 \, x^{10} - 5 \, x^{9}\right )} e^{4}\right )} \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((109350*x^5*exp(4)^4-510300*x^6*exp(4)^3+874800*x^7*exp(4)^2-656100*x^8*exp(4)+182250*x^9)*log(x)^2+
((-51030*x^6+36450*x^5)*exp(4)^4+(233280*x^7-145800*x^6)*exp(4)^3+(-393660*x^8+218700*x^7)*exp(4)^2+(291600*x^
9-145800*x^8)*exp(4)-80190*x^10+36450*x^9)*log(x)+(5832*x^7-7290*x^6)*exp(4)^4+(-26244*x^8+29160*x^7)*exp(4)^3
+(43740*x^9-43740*x^8)*exp(4)^2+(-32076*x^10+29160*x^9)*exp(4)+8748*x^11-7290*x^10,x, algorithm="maxima")

[Out]

729*x^12 + 729/2*(50*log(x)^2 - 10*log(x) + 1)*x^10 - 729/2*x^10*(8*e^4 + 1) - 900*(81*e^4*log(x)^2 - 18*e^4*l
og(x) + 2*e^4)*x^9 + 180*x^9*(27*e^8 + 10*e^4) + 54675/16*(32*e^8*log(x)^2 - 8*e^8*log(x) + e^8)*x^8 - 3645/16
*x^8*(16*e^12 + 15*e^8) - 72900/49*(49*e^12*log(x)^2 - 14*e^12*log(x) + 2*e^12)*x^7 + 7290/49*x^7*(7*e^16 + 20
*e^12) + 2025/2*(18*e^16*log(x)^2 - 6*e^16*log(x) + e^16)*x^6 - 2025/2*x^6*e^16 + 729/7*(7*x^8 - 10*x^7)*e^16
- 729*(4*x^9 - 5*x^8)*e^12 + 486*(9*x^10 - 10*x^9)*e^8 - 2916*(x^11 - x^10)*e^4 - 405/14*(252*x^11 - 126*x^10
+ 42*(6*x^7 - 5*x^6)*e^16 - 144*(7*x^8 - 5*x^7)*e^12 + 189*(8*x^9 - 5*x^8)*e^8 - 112*(9*x^10 - 5*x^9)*e^4)*log
(x)

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mupad [B]  time = 2.33, size = 21, normalized size = 0.88 \begin {gather*} 729\,x^6\,{\left (x-5\,\ln \relax (x)\right )}^2\,{\left (x-{\mathrm {e}}^4\right )}^4 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(log(x)*(exp(16)*(36450*x^5 - 51030*x^6) - exp(12)*(145800*x^6 - 233280*x^7) - exp(4)*(145800*x^8 - 291600*
x^9) + exp(8)*(218700*x^7 - 393660*x^8) + 36450*x^9 - 80190*x^10) - exp(16)*(7290*x^6 - 5832*x^7) + exp(12)*(2
9160*x^7 - 26244*x^8) + exp(4)*(29160*x^9 - 32076*x^10) - exp(8)*(43740*x^8 - 43740*x^9) + log(x)^2*(874800*x^
7*exp(8) - 656100*x^8*exp(4) - 510300*x^6*exp(12) + 109350*x^5*exp(16) + 182250*x^9) - 7290*x^10 + 8748*x^11,x
)

[Out]

729*x^6*(x - 5*log(x))^2*(x - exp(4))^4

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sympy [B]  time = 0.27, size = 124, normalized size = 5.17 \begin {gather*} 729 x^{12} - 2916 x^{11} e^{4} + 4374 x^{10} e^{8} - 2916 x^{9} e^{12} + 729 x^{8} e^{16} + \left (18225 x^{10} - 72900 x^{9} e^{4} + 109350 x^{8} e^{8} - 72900 x^{7} e^{12} + 18225 x^{6} e^{16}\right ) \log {\relax (x )}^{2} + \left (- 7290 x^{11} + 29160 x^{10} e^{4} - 43740 x^{9} e^{8} + 29160 x^{8} e^{12} - 7290 x^{7} e^{16}\right ) \log {\relax (x )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((109350*x**5*exp(4)**4-510300*x**6*exp(4)**3+874800*x**7*exp(4)**2-656100*x**8*exp(4)+182250*x**9)*l
n(x)**2+((-51030*x**6+36450*x**5)*exp(4)**4+(233280*x**7-145800*x**6)*exp(4)**3+(-393660*x**8+218700*x**7)*exp
(4)**2+(291600*x**9-145800*x**8)*exp(4)-80190*x**10+36450*x**9)*ln(x)+(5832*x**7-7290*x**6)*exp(4)**4+(-26244*
x**8+29160*x**7)*exp(4)**3+(43740*x**9-43740*x**8)*exp(4)**2+(-32076*x**10+29160*x**9)*exp(4)+8748*x**11-7290*
x**10,x)

[Out]

729*x**12 - 2916*x**11*exp(4) + 4374*x**10*exp(8) - 2916*x**9*exp(12) + 729*x**8*exp(16) + (18225*x**10 - 7290
0*x**9*exp(4) + 109350*x**8*exp(8) - 72900*x**7*exp(12) + 18225*x**6*exp(16))*log(x)**2 + (-7290*x**11 + 29160
*x**10*exp(4) - 43740*x**9*exp(8) + 29160*x**8*exp(12) - 7290*x**7*exp(16))*log(x)

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