3.2.64 \(\int \frac {-18 x^4-24 x^5-8 x^6+e^{10} (-18-24 x-8 x^2)+e^5 (36 x^2+48 x^3+16 x^4)+(e^{10} (-18-12 x)+108 x^4+156 x^5+56 x^6+e^5 (-90 x^2-144 x^3-56 x^4)) \log (x)+(-180 x^4-360 x^5-160 x^6+e^5 (120 x^3+80 x^4)) \log ^2(x)+(450 x^4+900 x^5+400 x^6) \log ^3(x)}{25 x^3 \log ^3(x)} \, dx\)

Optimal. Leaf size=32 \[ (3+2 x)^2 \left (-x+\frac {-\frac {e^5}{x}+x}{5 \log (x)}\right )^2 \]

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Rubi [F]  time = 1.07, 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 {-18 x^4-24 x^5-8 x^6+e^{10} \left (-18-24 x-8 x^2\right )+e^5 \left (36 x^2+48 x^3+16 x^4\right )+\left (e^{10} (-18-12 x)+108 x^4+156 x^5+56 x^6+e^5 \left (-90 x^2-144 x^3-56 x^4\right )\right ) \log (x)+\left (-180 x^4-360 x^5-160 x^6+e^5 \left (120 x^3+80 x^4\right )\right ) \log ^2(x)+\left (450 x^4+900 x^5+400 x^6\right ) \log ^3(x)}{25 x^3 \log ^3(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-18*x^4 - 24*x^5 - 8*x^6 + E^10*(-18 - 24*x - 8*x^2) + E^5*(36*x^2 + 48*x^3 + 16*x^4) + (E^10*(-18 - 12*x
) + 108*x^4 + 156*x^5 + 56*x^6 + E^5*(-90*x^2 - 144*x^3 - 56*x^4))*Log[x] + (-180*x^4 - 360*x^5 - 160*x^6 + E^
5*(120*x^3 + 80*x^4))*Log[x]^2 + (450*x^4 + 900*x^5 + 400*x^6)*Log[x]^3)/(25*x^3*Log[x]^3),x]

[Out]

x^2*(3 + 2*x)^2 - (4*(9 - 4*E^5)*ExpIntegralEi[2*Log[x]])/5 - (72*ExpIntegralEi[3*Log[x]])/5 - (32*ExpIntegral
Ei[4*Log[x]])/5 + (24*E^5*LogIntegral[x])/5 - (2*Defer[Int][((3 + 2*x)^2*(-E^5 + x^2)^2)/(x^3*Log[x]^3), x])/2
5 + (2*Defer[Int][((3 + 2*x)*(-E^5 + x^2)*(3*E^5 + 18*x^2 + 14*x^3))/(x^3*Log[x]^2), x])/25

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{25} \int \frac {-18 x^4-24 x^5-8 x^6+e^{10} \left (-18-24 x-8 x^2\right )+e^5 \left (36 x^2+48 x^3+16 x^4\right )+\left (e^{10} (-18-12 x)+108 x^4+156 x^5+56 x^6+e^5 \left (-90 x^2-144 x^3-56 x^4\right )\right ) \log (x)+\left (-180 x^4-360 x^5-160 x^6+e^5 \left (120 x^3+80 x^4\right )\right ) \log ^2(x)+\left (450 x^4+900 x^5+400 x^6\right ) \log ^3(x)}{x^3 \log ^3(x)} \, dx\\ &=\frac {1}{25} \int \frac {2 (3+2 x) \left (-\left ((3+2 x) \left (e^5-x^2\right )^2\right )-\left (3 e^{10}-2 x^4 (9+7 x)+e^5 x^2 (15+14 x)\right ) \log (x)-10 x^3 \left (-2 e^5+x (3+4 x)\right ) \log ^2(x)+25 x^4 (3+4 x) \log ^3(x)\right )}{x^3 \log ^3(x)} \, dx\\ &=\frac {2}{25} \int \frac {(3+2 x) \left (-\left ((3+2 x) \left (e^5-x^2\right )^2\right )-\left (3 e^{10}-2 x^4 (9+7 x)+e^5 x^2 (15+14 x)\right ) \log (x)-10 x^3 \left (-2 e^5+x (3+4 x)\right ) \log ^2(x)+25 x^4 (3+4 x) \log ^3(x)\right )}{x^3 \log ^3(x)} \, dx\\ &=\frac {2}{25} \int \left (25 x (3+2 x) (3+4 x)-\frac {(3+2 x)^2 \left (-e^5+x^2\right )^2}{x^3 \log ^3(x)}+\frac {(3+2 x) \left (-e^5+x^2\right ) \left (3 e^5+18 x^2+14 x^3\right )}{x^3 \log ^2(x)}-\frac {10 (3+2 x) \left (-2 e^5+3 x+4 x^2\right )}{\log (x)}\right ) \, dx\\ &=-\left (\frac {2}{25} \int \frac {(3+2 x)^2 \left (-e^5+x^2\right )^2}{x^3 \log ^3(x)} \, dx\right )+\frac {2}{25} \int \frac {(3+2 x) \left (-e^5+x^2\right ) \left (3 e^5+18 x^2+14 x^3\right )}{x^3 \log ^2(x)} \, dx-\frac {4}{5} \int \frac {(3+2 x) \left (-2 e^5+3 x+4 x^2\right )}{\log (x)} \, dx+2 \int x (3+2 x) (3+4 x) \, dx\\ &=x^2 (3+2 x)^2-\frac {2}{25} \int \frac {(3+2 x)^2 \left (-e^5+x^2\right )^2}{x^3 \log ^3(x)} \, dx+\frac {2}{25} \int \frac {(3+2 x) \left (-e^5+x^2\right ) \left (3 e^5+18 x^2+14 x^3\right )}{x^3 \log ^2(x)} \, dx-\frac {4}{5} \int \left (-\frac {6 e^5}{\log (x)}+\frac {\left (9-4 e^5\right ) x}{\log (x)}+\frac {18 x^2}{\log (x)}+\frac {8 x^3}{\log (x)}\right ) \, dx\\ &=x^2 (3+2 x)^2-\frac {2}{25} \int \frac {(3+2 x)^2 \left (-e^5+x^2\right )^2}{x^3 \log ^3(x)} \, dx+\frac {2}{25} \int \frac {(3+2 x) \left (-e^5+x^2\right ) \left (3 e^5+18 x^2+14 x^3\right )}{x^3 \log ^2(x)} \, dx-\frac {32}{5} \int \frac {x^3}{\log (x)} \, dx-\frac {72}{5} \int \frac {x^2}{\log (x)} \, dx+\frac {1}{5} \left (24 e^5\right ) \int \frac {1}{\log (x)} \, dx-\frac {1}{5} \left (4 \left (9-4 e^5\right )\right ) \int \frac {x}{\log (x)} \, dx\\ &=x^2 (3+2 x)^2+\frac {24 e^5 \text {li}(x)}{5}-\frac {2}{25} \int \frac {(3+2 x)^2 \left (-e^5+x^2\right )^2}{x^3 \log ^3(x)} \, dx+\frac {2}{25} \int \frac {(3+2 x) \left (-e^5+x^2\right ) \left (3 e^5+18 x^2+14 x^3\right )}{x^3 \log ^2(x)} \, dx-\frac {32}{5} \operatorname {Subst}\left (\int \frac {e^{4 x}}{x} \, dx,x,\log (x)\right )-\frac {72}{5} \operatorname {Subst}\left (\int \frac {e^{3 x}}{x} \, dx,x,\log (x)\right )-\frac {1}{5} \left (4 \left (9-4 e^5\right )\right ) \operatorname {Subst}\left (\int \frac {e^{2 x}}{x} \, dx,x,\log (x)\right )\\ &=x^2 (3+2 x)^2-\frac {4}{5} \left (9-4 e^5\right ) \text {Ei}(2 \log (x))-\frac {72}{5} \text {Ei}(3 \log (x))-\frac {32}{5} \text {Ei}(4 \log (x))+\frac {24 e^5 \text {li}(x)}{5}-\frac {2}{25} \int \frac {(3+2 x)^2 \left (-e^5+x^2\right )^2}{x^3 \log ^3(x)} \, dx+\frac {2}{25} \int \frac {(3+2 x) \left (-e^5+x^2\right ) \left (3 e^5+18 x^2+14 x^3\right )}{x^3 \log ^2(x)} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.07, size = 36, normalized size = 1.12 \begin {gather*} \frac {(3+2 x)^2 \left (e^5-x^2+5 x^2 \log (x)\right )^2}{25 x^2 \log ^2(x)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-18*x^4 - 24*x^5 - 8*x^6 + E^10*(-18 - 24*x - 8*x^2) + E^5*(36*x^2 + 48*x^3 + 16*x^4) + (E^10*(-18
- 12*x) + 108*x^4 + 156*x^5 + 56*x^6 + E^5*(-90*x^2 - 144*x^3 - 56*x^4))*Log[x] + (-180*x^4 - 360*x^5 - 160*x^
6 + E^5*(120*x^3 + 80*x^4))*Log[x]^2 + (450*x^4 + 900*x^5 + 400*x^6)*Log[x]^3)/(25*x^3*Log[x]^3),x]

[Out]

((3 + 2*x)^2*(E^5 - x^2 + 5*x^2*Log[x])^2)/(25*x^2*Log[x]^2)

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fricas [B]  time = 1.14, size = 120, normalized size = 3.75 \begin {gather*} \frac {4 \, x^{6} + 12 \, x^{5} + 9 \, x^{4} + 25 \, {\left (4 \, x^{6} + 12 \, x^{5} + 9 \, x^{4}\right )} \log \relax (x)^{2} + {\left (4 \, x^{2} + 12 \, x + 9\right )} e^{10} - 2 \, {\left (4 \, x^{4} + 12 \, x^{3} + 9 \, x^{2}\right )} e^{5} - 10 \, {\left (4 \, x^{6} + 12 \, x^{5} + 9 \, x^{4} - {\left (4 \, x^{4} + 12 \, x^{3} + 9 \, x^{2}\right )} e^{5}\right )} \log \relax (x)}{25 \, x^{2} \log \relax (x)^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/25*((400*x^6+900*x^5+450*x^4)*log(x)^3+((80*x^4+120*x^3)*exp(5)-160*x^6-360*x^5-180*x^4)*log(x)^2+
((-12*x-18)*exp(5)^2+(-56*x^4-144*x^3-90*x^2)*exp(5)+56*x^6+156*x^5+108*x^4)*log(x)+(-8*x^2-24*x-18)*exp(5)^2+
(16*x^4+48*x^3+36*x^2)*exp(5)-8*x^6-24*x^5-18*x^4)/x^3/log(x)^3,x, algorithm="fricas")

[Out]

1/25*(4*x^6 + 12*x^5 + 9*x^4 + 25*(4*x^6 + 12*x^5 + 9*x^4)*log(x)^2 + (4*x^2 + 12*x + 9)*e^10 - 2*(4*x^4 + 12*
x^3 + 9*x^2)*e^5 - 10*(4*x^6 + 12*x^5 + 9*x^4 - (4*x^4 + 12*x^3 + 9*x^2)*e^5)*log(x))/(x^2*log(x)^2)

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giac [B]  time = 0.46, size = 137, normalized size = 4.28 \begin {gather*} \frac {100 \, x^{6} \log \relax (x)^{2} - 40 \, x^{6} \log \relax (x) + 300 \, x^{5} \log \relax (x)^{2} + 4 \, x^{6} - 120 \, x^{5} \log \relax (x) + 40 \, x^{4} e^{5} \log \relax (x) + 225 \, x^{4} \log \relax (x)^{2} + 12 \, x^{5} - 8 \, x^{4} e^{5} - 90 \, x^{4} \log \relax (x) + 120 \, x^{3} e^{5} \log \relax (x) + 9 \, x^{4} - 24 \, x^{3} e^{5} + 90 \, x^{2} e^{5} \log \relax (x) + 4 \, x^{2} e^{10} - 18 \, x^{2} e^{5} + 12 \, x e^{10} + 9 \, e^{10}}{25 \, x^{2} \log \relax (x)^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/25*((400*x^6+900*x^5+450*x^4)*log(x)^3+((80*x^4+120*x^3)*exp(5)-160*x^6-360*x^5-180*x^4)*log(x)^2+
((-12*x-18)*exp(5)^2+(-56*x^4-144*x^3-90*x^2)*exp(5)+56*x^6+156*x^5+108*x^4)*log(x)+(-8*x^2-24*x-18)*exp(5)^2+
(16*x^4+48*x^3+36*x^2)*exp(5)-8*x^6-24*x^5-18*x^4)/x^3/log(x)^3,x, algorithm="giac")

[Out]

1/25*(100*x^6*log(x)^2 - 40*x^6*log(x) + 300*x^5*log(x)^2 + 4*x^6 - 120*x^5*log(x) + 40*x^4*e^5*log(x) + 225*x
^4*log(x)^2 + 12*x^5 - 8*x^4*e^5 - 90*x^4*log(x) + 120*x^3*e^5*log(x) + 9*x^4 - 24*x^3*e^5 + 90*x^2*e^5*log(x)
+ 4*x^2*e^10 - 18*x^2*e^5 + 12*x*e^10 + 9*e^10)/(x^2*log(x)^2)

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maple [B]  time = 0.04, size = 127, normalized size = 3.97

method	result	size
risch	\(4 x^{4}+12 x^{3}+9 x^{2}+\frac {-40 x^{6} \ln \relax (x )+40 \ln \relax (x ) {\mathrm e}^{5} x^{4}+4 x^{6}-120 x^{5} \ln \relax (x )-8 x^{4} {\mathrm e}^{5}+120 x^{3} {\mathrm e}^{5} \ln \relax (x )+12 x^{5}-90 x^{4} \ln \relax (x )+4 \,{\mathrm e}^{10} x^{2}-24 x^{3} {\mathrm e}^{5}+90 x^{2} {\mathrm e}^{5} \ln \relax (x )+9 x^{4}+12 x \,{\mathrm e}^{10}-18 x^{2} {\mathrm e}^{5}+9 \,{\mathrm e}^{10}}{25 x^{2} \ln \relax (x )^{2}}\)	\(127\)
default	\(-\frac {18 x^{2}}{5 \ln \relax (x )}+4 x^{4}+12 x^{3}+9 x^{2}+\frac {9 x^{2}}{25 \ln \relax (x )^{2}}-\frac {8 x^{4}}{5 \ln \relax (x )}-\frac {24 x^{3}}{5 \ln \relax (x )}+\frac {48 \,{\mathrm e}^{5} \left (-\frac {x}{2 \ln \relax (x )^{2}}-\frac {x}{2 \ln \relax (x )}-\frac {\expIntegralEi \left (1, -\ln \relax (x )\right )}{2}\right )}{25}-\frac {18 \,{\mathrm e}^{10} \left (-\frac {1}{x^{2} \ln \relax (x )}+2 \expIntegralEi \left (1, 2 \ln \relax (x )\right )\right )}{25}-\frac {16 \,{\mathrm e}^{5} \expIntegralEi \left (1, -2 \ln \relax (x )\right )}{5}-\frac {24 \,{\mathrm e}^{5} \expIntegralEi \left (1, -\ln \relax (x )\right )}{5}-\frac {56 \,{\mathrm e}^{5} \left (-\frac {x^{2}}{\ln \relax (x )}-2 \expIntegralEi \left (1, -2 \ln \relax (x )\right )\right )}{25}-\frac {18 \,{\mathrm e}^{10} \left (-\frac {1}{2 x^{2} \ln \relax (x )^{2}}+\frac {1}{x^{2} \ln \relax (x )}-2 \expIntegralEi \left (1, 2 \ln \relax (x )\right )\right )}{25}+\frac {16 \,{\mathrm e}^{5} \left (-\frac {x^{2}}{2 \ln \relax (x )^{2}}-\frac {x^{2}}{\ln \relax (x )}-2 \expIntegralEi \left (1, -2 \ln \relax (x )\right )\right )}{25}+\frac {4 \,{\mathrm e}^{10}}{25 \ln \relax (x )^{2}}-\frac {24 \,{\mathrm e}^{10} \left (-\frac {1}{2 x \ln \relax (x )^{2}}+\frac {1}{2 x \ln \relax (x )}-\frac {\expIntegralEi \left (1, \ln \relax (x )\right )}{2}\right )}{25}-\frac {144 \,{\mathrm e}^{5} \left (-\frac {x}{\ln \relax (x )}-\expIntegralEi \left (1, -\ln \relax (x )\right )\right )}{25}-\frac {12 \,{\mathrm e}^{10} \left (-\frac {1}{x \ln \relax (x )}+\expIntegralEi \left (1, \ln \relax (x )\right )\right )}{25}+\frac {4 x^{4}}{25 \ln \relax (x )^{2}}+\frac {12 x^{3}}{25 \ln \relax (x )^{2}}-\frac {18 \,{\mathrm e}^{5}}{25 \ln \relax (x )^{2}}+\frac {18 \,{\mathrm e}^{5}}{5 \ln \relax (x )}\)	\(324\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/25*((400*x^6+900*x^5+450*x^4)*ln(x)^3+((80*x^4+120*x^3)*exp(5)-160*x^6-360*x^5-180*x^4)*ln(x)^2+((-12*x-
18)*exp(5)^2+(-56*x^4-144*x^3-90*x^2)*exp(5)+56*x^6+156*x^5+108*x^4)*ln(x)+(-8*x^2-24*x-18)*exp(5)^2+(16*x^4+4
8*x^3+36*x^2)*exp(5)-8*x^6-24*x^5-18*x^4)/x^3/ln(x)^3,x,method=_RETURNVERBOSE)

[Out]

4*x^4+12*x^3+9*x^2+1/25*(-40*x^6*ln(x)+40*ln(x)*exp(5)*x^4+4*x^6-120*x^5*ln(x)-8*x^4*exp(5)+120*x^3*exp(5)*ln(
x)+12*x^5-90*x^4*ln(x)+4*exp(10)*x^2-24*x^3*exp(5)+90*x^2*exp(5)*ln(x)+9*x^4+12*x*exp(10)-18*x^2*exp(5)+9*exp(
10))/x^2/ln(x)^2

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maxima [C]  time = 0.75, size = 201, normalized size = 6.28 \begin {gather*} 4 \, x^{4} + 12 \, x^{3} + 9 \, x^{2} + \frac {16}{5} \, {\rm Ei}\left (2 \, \log \relax (x)\right ) e^{5} + \frac {24}{5} \, {\rm Ei}\left (\log \relax (x)\right ) e^{5} + \frac {36}{25} \, e^{10} \Gamma \left (-1, 2 \, \log \relax (x)\right ) - \frac {144}{25} \, e^{5} \Gamma \left (-1, -\log \relax (x)\right ) - \frac {112}{25} \, e^{5} \Gamma \left (-1, -2 \, \log \relax (x)\right ) + \frac {12}{25} \, e^{10} \Gamma \left (-1, \log \relax (x)\right ) + \frac {72}{25} \, e^{10} \Gamma \left (-2, 2 \, \log \relax (x)\right ) - \frac {48}{25} \, e^{5} \Gamma \left (-2, -\log \relax (x)\right ) - \frac {64}{25} \, e^{5} \Gamma \left (-2, -2 \, \log \relax (x)\right ) + \frac {24}{25} \, e^{10} \Gamma \left (-2, \log \relax (x)\right ) + \frac {18 \, e^{5}}{5 \, \log \relax (x)} + \frac {4 \, e^{10}}{25 \, \log \relax (x)^{2}} - \frac {18 \, e^{5}}{25 \, \log \relax (x)^{2}} - \frac {32}{5} \, {\rm Ei}\left (4 \, \log \relax (x)\right ) - \frac {72}{5} \, {\rm Ei}\left (3 \, \log \relax (x)\right ) - \frac {36}{5} \, {\rm Ei}\left (2 \, \log \relax (x)\right ) + \frac {216}{25} \, \Gamma \left (-1, -2 \, \log \relax (x)\right ) + \frac {468}{25} \, \Gamma \left (-1, -3 \, \log \relax (x)\right ) + \frac {224}{25} \, \Gamma \left (-1, -4 \, \log \relax (x)\right ) + \frac {72}{25} \, \Gamma \left (-2, -2 \, \log \relax (x)\right ) + \frac {216}{25} \, \Gamma \left (-2, -3 \, \log \relax (x)\right ) + \frac {128}{25} \, \Gamma \left (-2, -4 \, \log \relax (x)\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/25*((400*x^6+900*x^5+450*x^4)*log(x)^3+((80*x^4+120*x^3)*exp(5)-160*x^6-360*x^5-180*x^4)*log(x)^2+
((-12*x-18)*exp(5)^2+(-56*x^4-144*x^3-90*x^2)*exp(5)+56*x^6+156*x^5+108*x^4)*log(x)+(-8*x^2-24*x-18)*exp(5)^2+
(16*x^4+48*x^3+36*x^2)*exp(5)-8*x^6-24*x^5-18*x^4)/x^3/log(x)^3,x, algorithm="maxima")

[Out]

4*x^4 + 12*x^3 + 9*x^2 + 16/5*Ei(2*log(x))*e^5 + 24/5*Ei(log(x))*e^5 + 36/25*e^10*gamma(-1, 2*log(x)) - 144/25
*e^5*gamma(-1, -log(x)) - 112/25*e^5*gamma(-1, -2*log(x)) + 12/25*e^10*gamma(-1, log(x)) + 72/25*e^10*gamma(-2
, 2*log(x)) - 48/25*e^5*gamma(-2, -log(x)) - 64/25*e^5*gamma(-2, -2*log(x)) + 24/25*e^10*gamma(-2, log(x)) + 1
8/5*e^5/log(x) + 4/25*e^10/log(x)^2 - 18/25*e^5/log(x)^2 - 32/5*Ei(4*log(x)) - 72/5*Ei(3*log(x)) - 36/5*Ei(2*l
og(x)) + 216/25*gamma(-1, -2*log(x)) + 468/25*gamma(-1, -3*log(x)) + 224/25*gamma(-1, -4*log(x)) + 72/25*gamma
(-2, -2*log(x)) + 216/25*gamma(-2, -3*log(x)) + 128/25*gamma(-2, -4*log(x))

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mupad [B]  time = 0.50, size = 33, normalized size = 1.03 \begin {gather*} \frac {{\left (2\,x+3\right )}^2\,{\left ({\mathrm {e}}^5+5\,x^2\,\ln \relax (x)-x^2\right )}^2}{25\,x^2\,{\ln \relax (x)}^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-((exp(10)*(24*x + 8*x^2 + 18))/25 - (log(x)*(108*x^4 - exp(5)*(90*x^2 + 144*x^3 + 56*x^4) + 156*x^5 + 56*
x^6 - exp(10)*(12*x + 18)))/25 + (log(x)^2*(180*x^4 - exp(5)*(120*x^3 + 80*x^4) + 360*x^5 + 160*x^6))/25 - (lo
g(x)^3*(450*x^4 + 900*x^5 + 400*x^6))/25 - (exp(5)*(36*x^2 + 48*x^3 + 16*x^4))/25 + (18*x^4)/25 + (24*x^5)/25
+ (8*x^6)/25)/(x^3*log(x)^3),x)

[Out]

((2*x + 3)^2*(exp(5) + 5*x^2*log(x) - x^2)^2)/(25*x^2*log(x)^2)

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sympy [B]  time = 0.22, size = 129, normalized size = 4.03 \begin {gather*} 4 x^{4} + 12 x^{3} + 9 x^{2} + \frac {4 x^{6} + 12 x^{5} - 8 x^{4} e^{5} + 9 x^{4} - 24 x^{3} e^{5} - 18 x^{2} e^{5} + 4 x^{2} e^{10} + 12 x e^{10} + \left (- 40 x^{6} - 120 x^{5} - 90 x^{4} + 40 x^{4} e^{5} + 120 x^{3} e^{5} + 90 x^{2} e^{5}\right ) \log {\relax (x )} + 9 e^{10}}{25 x^{2} \log {\relax (x )}^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/25*((400*x**6+900*x**5+450*x**4)*ln(x)**3+((80*x**4+120*x**3)*exp(5)-160*x**6-360*x**5-180*x**4)*l
n(x)**2+((-12*x-18)*exp(5)**2+(-56*x**4-144*x**3-90*x**2)*exp(5)+56*x**6+156*x**5+108*x**4)*ln(x)+(-8*x**2-24*
x-18)*exp(5)**2+(16*x**4+48*x**3+36*x**2)*exp(5)-8*x**6-24*x**5-18*x**4)/x**3/ln(x)**3,x)

[Out]

4*x**4 + 12*x**3 + 9*x**2 + (4*x**6 + 12*x**5 - 8*x**4*exp(5) + 9*x**4 - 24*x**3*exp(5) - 18*x**2*exp(5) + 4*x
**2*exp(10) + 12*x*exp(10) + (-40*x**6 - 120*x**5 - 90*x**4 + 40*x**4*exp(5) + 120*x**3*exp(5) + 90*x**2*exp(5
))*log(x) + 9*exp(10))/(25*x**2*log(x)**2)

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