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3.4.56 \(\int \frac {-200 x-1592 x^2+96 x^3+256 x^4+e^3 (-40 x-320 x^2)+(2000+400 e^3-80 x-320 x^2) \log (x)+(-40 x-320 x^2) \log ^2(x)+400 \log ^3(x)}{381924 x+625 e^{12} x-61800 x^2-243464 x^3+29788 x^4+58577 x^5-4784 x^6-6304 x^7+256 x^8+256 x^9+e^9 (12500 x-500 x^2-2000 x^3)+e^6 (93400 x-7500 x^2-29850 x^3+1200 x^4+2400 x^5)+e^3 (309000 x-37360 x^2-147940 x^3+11980 x^4+23760 x^5-960 x^6-1280 x^7)+(309000 x+2500 e^9 x-37360 x^2-147940 x^3+11980 x^4+23760 x^5-960 x^6-1280 x^7+e^6 (37500 x-1500 x^2-6000 x^3)+e^3 (186800 x-15000 x^2-59700 x^3+2400 x^4+4800 x^5)) \log ^2(x)+(93400 x+3750 e^6 x-7500 x^2-29850 x^3+1200 x^4+2400 x^5+e^3 (37500 x-1500 x^2-6000 x^3)) \log ^4(x)+(12500 x+2500 e^3 x-500 x^2-2000 x^3) \log ^6(x)+625 x \log ^8(x)} \, dx\)

Optimal. Leaf size=28 \[ \frac {4}{7-\left (x+4 x^2-5 \left (5+e^3+\log ^2(x)\right )\right )^2} \]

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Rubi [F]  time = 7.78, 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 {-200 x-1592 x^2+96 x^3+256 x^4+e^3 \left (-40 x-320 x^2\right )+\left (2000+400 e^3-80 x-320 x^2\right ) \log (x)+\left (-40 x-320 x^2\right ) \log ^2(x)+400 \log ^3(x)}{381924 x+625 e^{12} x-61800 x^2-243464 x^3+29788 x^4+58577 x^5-4784 x^6-6304 x^7+256 x^8+256 x^9+e^9 \left (12500 x-500 x^2-2000 x^3\right )+e^6 \left (93400 x-7500 x^2-29850 x^3+1200 x^4+2400 x^5\right )+e^3 \left (309000 x-37360 x^2-147940 x^3+11980 x^4+23760 x^5-960 x^6-1280 x^7\right )+\left (309000 x+2500 e^9 x-37360 x^2-147940 x^3+11980 x^4+23760 x^5-960 x^6-1280 x^7+e^6 \left (37500 x-1500 x^2-6000 x^3\right )+e^3 \left (186800 x-15000 x^2-59700 x^3+2400 x^4+4800 x^5\right )\right ) \log ^2(x)+\left (93400 x+3750 e^6 x-7500 x^2-29850 x^3+1200 x^4+2400 x^5+e^3 \left (37500 x-1500 x^2-6000 x^3\right )\right ) \log ^4(x)+\left (12500 x+2500 e^3 x-500 x^2-2000 x^3\right ) \log ^6(x)+625 x \log ^8(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-200*x - 1592*x^2 + 96*x^3 + 256*x^4 + E^3*(-40*x - 320*x^2) + (2000 + 400*E^3 - 80*x - 320*x^2)*Log[x] +
 (-40*x - 320*x^2)*Log[x]^2 + 400*Log[x]^3)/(381924*x + 625*E^12*x - 61800*x^2 - 243464*x^3 + 29788*x^4 + 5857
7*x^5 - 4784*x^6 - 6304*x^7 + 256*x^8 + 256*x^9 + E^9*(12500*x - 500*x^2 - 2000*x^3) + E^6*(93400*x - 7500*x^2
 - 29850*x^3 + 1200*x^4 + 2400*x^5) + E^3*(309000*x - 37360*x^2 - 147940*x^3 + 11980*x^4 + 23760*x^5 - 960*x^6
 - 1280*x^7) + (309000*x + 2500*E^9*x - 37360*x^2 - 147940*x^3 + 11980*x^4 + 23760*x^5 - 960*x^6 - 1280*x^7 +
E^6*(37500*x - 1500*x^2 - 6000*x^3) + E^3*(186800*x - 15000*x^2 - 59700*x^3 + 2400*x^4 + 4800*x^5))*Log[x]^2 +
 (93400*x + 3750*E^6*x - 7500*x^2 - 29850*x^3 + 1200*x^4 + 2400*x^5 + E^3*(37500*x - 1500*x^2 - 6000*x^3))*Log
[x]^4 + (12500*x + 2500*E^3*x - 500*x^2 - 2000*x^3)*Log[x]^6 + 625*x*Log[x]^8),x]

[Out]

-40*(5 + E^3)*Defer[Int][(618*(1 + (25*E^3*(10 + E^3))/618) - 50*(1 + E^3/5)*x - 199*(1 + (40*E^3)/199)*x^2 +
8*x^3 + 16*x^4 + 250*(1 + E^3/5)*Log[x]^2 - 10*x*Log[x]^2 - 40*x^2*Log[x]^2 + 25*Log[x]^4)^(-2), x] - 8*(199 +
 40*E^3)*Defer[Int][x/(618*(1 + (25*E^3*(10 + E^3))/618) - 50*(1 + E^3/5)*x - 199*(1 + (40*E^3)/199)*x^2 + 8*x
^3 + 16*x^4 + 250*(1 + E^3/5)*Log[x]^2 - 10*x*Log[x]^2 - 40*x^2*Log[x]^2 + 25*Log[x]^4)^2, x] + 96*Defer[Int][
x^2/(618*(1 + (25*E^3*(10 + E^3))/618) - 50*(1 + E^3/5)*x - 199*(1 + (40*E^3)/199)*x^2 + 8*x^3 + 16*x^4 + 250*
(1 + E^3/5)*Log[x]^2 - 10*x*Log[x]^2 - 40*x^2*Log[x]^2 + 25*Log[x]^4)^2, x] + 256*Defer[Int][x^3/(618*(1 + (25
*E^3*(10 + E^3))/618) - 50*(1 + E^3/5)*x - 199*(1 + (40*E^3)/199)*x^2 + 8*x^3 + 16*x^4 + 250*(1 + E^3/5)*Log[x
]^2 - 10*x*Log[x]^2 - 40*x^2*Log[x]^2 + 25*Log[x]^4)^2, x] - 80*Defer[Int][Log[x]/(618*(1 + (25*E^3*(10 + E^3)
)/618) - 50*(1 + E^3/5)*x - 199*(1 + (40*E^3)/199)*x^2 + 8*x^3 + 16*x^4 + 250*(1 + E^3/5)*Log[x]^2 - 10*x*Log[
x]^2 - 40*x^2*Log[x]^2 + 25*Log[x]^4)^2, x] + 400*(5 + E^3)*Defer[Int][Log[x]/(x*(618*(1 + (25*E^3*(10 + E^3))
/618) - 50*(1 + E^3/5)*x - 199*(1 + (40*E^3)/199)*x^2 + 8*x^3 + 16*x^4 + 250*(1 + E^3/5)*Log[x]^2 - 10*x*Log[x
]^2 - 40*x^2*Log[x]^2 + 25*Log[x]^4)^2), x] - 320*Defer[Int][(x*Log[x])/(618*(1 + (25*E^3*(10 + E^3))/618) - 5
0*(1 + E^3/5)*x - 199*(1 + (40*E^3)/199)*x^2 + 8*x^3 + 16*x^4 + 250*(1 + E^3/5)*Log[x]^2 - 10*x*Log[x]^2 - 40*
x^2*Log[x]^2 + 25*Log[x]^4)^2, x] - 40*Defer[Int][Log[x]^2/(618*(1 + (25*E^3*(10 + E^3))/618) - 50*(1 + E^3/5)
*x - 199*(1 + (40*E^3)/199)*x^2 + 8*x^3 + 16*x^4 + 250*(1 + E^3/5)*Log[x]^2 - 10*x*Log[x]^2 - 40*x^2*Log[x]^2
+ 25*Log[x]^4)^2, x] - 320*Defer[Int][(x*Log[x]^2)/(618*(1 + (25*E^3*(10 + E^3))/618) - 50*(1 + E^3/5)*x - 199
*(1 + (40*E^3)/199)*x^2 + 8*x^3 + 16*x^4 + 250*(1 + E^3/5)*Log[x]^2 - 10*x*Log[x]^2 - 40*x^2*Log[x]^2 + 25*Log
[x]^4)^2, x] + 400*Defer[Int][Log[x]^3/(x*(618*(1 + (25*E^3*(10 + E^3))/618) - 50*(1 + E^3/5)*x - 199*(1 + (40
*E^3)/199)*x^2 + 8*x^3 + 16*x^4 + 250*(1 + E^3/5)*Log[x]^2 - 10*x*Log[x]^2 - 40*x^2*Log[x]^2 + 25*Log[x]^4)^2)
, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-200 x-1592 x^2+96 x^3+256 x^4+e^3 \left (-40 x-320 x^2\right )+\left (2000+400 e^3-80 x-320 x^2\right ) \log (x)+\left (-40 x-320 x^2\right ) \log ^2(x)+400 \log ^3(x)}{\left (381924+625 e^{12}\right ) x-61800 x^2-243464 x^3+29788 x^4+58577 x^5-4784 x^6-6304 x^7+256 x^8+256 x^9+e^9 \left (12500 x-500 x^2-2000 x^3\right )+e^6 \left (93400 x-7500 x^2-29850 x^3+1200 x^4+2400 x^5\right )+e^3 \left (309000 x-37360 x^2-147940 x^3+11980 x^4+23760 x^5-960 x^6-1280 x^7\right )+\left (309000 x+2500 e^9 x-37360 x^2-147940 x^3+11980 x^4+23760 x^5-960 x^6-1280 x^7+e^6 \left (37500 x-1500 x^2-6000 x^3\right )+e^3 \left (186800 x-15000 x^2-59700 x^3+2400 x^4+4800 x^5\right )\right ) \log ^2(x)+\left (93400 x+3750 e^6 x-7500 x^2-29850 x^3+1200 x^4+2400 x^5+e^3 \left (37500 x-1500 x^2-6000 x^3\right )\right ) \log ^4(x)+\left (12500 x+2500 e^3 x-500 x^2-2000 x^3\right ) \log ^6(x)+625 x \log ^8(x)} \, dx\\ &=\int \frac {8 \left (x+8 x^2-10 \log (x)\right ) \left (-25 \left (1+\frac {e^3}{5}\right )+x+4 x^2-5 \log ^2(x)\right )}{x \left (618 \left (1+\frac {25 e^6}{618}\right )-50 x-199 x^2+8 x^3+16 x^4-10 e^3 \left (-25+x+4 x^2\right )+10 \left (25+5 e^3-x-4 x^2\right ) \log ^2(x)+25 \log ^4(x)\right )^2} \, dx\\ &=8 \int \frac {\left (x+8 x^2-10 \log (x)\right ) \left (-25 \left (1+\frac {e^3}{5}\right )+x+4 x^2-5 \log ^2(x)\right )}{x \left (618 \left (1+\frac {25 e^6}{618}\right )-50 x-199 x^2+8 x^3+16 x^4-10 e^3 \left (-25+x+4 x^2\right )+10 \left (25+5 e^3-x-4 x^2\right ) \log ^2(x)+25 \log ^4(x)\right )^2} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.08, size = 69, normalized size = 2.46 \begin {gather*} -\frac {4}{618+25 e^6-50 x-199 x^2+8 x^3+16 x^4-10 e^3 \left (-25+x+4 x^2\right )+10 \left (25+5 e^3-x-4 x^2\right ) \log ^2(x)+25 \log ^4(x)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-200*x - 1592*x^2 + 96*x^3 + 256*x^4 + E^3*(-40*x - 320*x^2) + (2000 + 400*E^3 - 80*x - 320*x^2)*Lo
g[x] + (-40*x - 320*x^2)*Log[x]^2 + 400*Log[x]^3)/(381924*x + 625*E^12*x - 61800*x^2 - 243464*x^3 + 29788*x^4
+ 58577*x^5 - 4784*x^6 - 6304*x^7 + 256*x^8 + 256*x^9 + E^9*(12500*x - 500*x^2 - 2000*x^3) + E^6*(93400*x - 75
00*x^2 - 29850*x^3 + 1200*x^4 + 2400*x^5) + E^3*(309000*x - 37360*x^2 - 147940*x^3 + 11980*x^4 + 23760*x^5 - 9
60*x^6 - 1280*x^7) + (309000*x + 2500*E^9*x - 37360*x^2 - 147940*x^3 + 11980*x^4 + 23760*x^5 - 960*x^6 - 1280*
x^7 + E^6*(37500*x - 1500*x^2 - 6000*x^3) + E^3*(186800*x - 15000*x^2 - 59700*x^3 + 2400*x^4 + 4800*x^5))*Log[
x]^2 + (93400*x + 3750*E^6*x - 7500*x^2 - 29850*x^3 + 1200*x^4 + 2400*x^5 + E^3*(37500*x - 1500*x^2 - 6000*x^3
))*Log[x]^4 + (12500*x + 2500*E^3*x - 500*x^2 - 2000*x^3)*Log[x]^6 + 625*x*Log[x]^8),x]

[Out]

-4/(618 + 25*E^6 - 50*x - 199*x^2 + 8*x^3 + 16*x^4 - 10*E^3*(-25 + x + 4*x^2) + 10*(25 + 5*E^3 - x - 4*x^2)*Lo
g[x]^2 + 25*Log[x]^4)

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fricas [B]  time = 0.69, size = 64, normalized size = 2.29 \begin {gather*} -\frac {4}{16 \, x^{4} + 25 \, \log \relax (x)^{4} + 8 \, x^{3} - 10 \, {\left (4 \, x^{2} + x - 5 \, e^{3} - 25\right )} \log \relax (x)^{2} - 199 \, x^{2} - 10 \, {\left (4 \, x^{2} + x - 25\right )} e^{3} - 50 \, x + 25 \, e^{6} + 618} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((400*log(x)^3+(-320*x^2-40*x)*log(x)^2+(400*exp(3)-320*x^2-80*x+2000)*log(x)+(-320*x^2-40*x)*exp(3)+
256*x^4+96*x^3-1592*x^2-200*x)/(625*x*log(x)^8+(2500*x*exp(3)-2000*x^3-500*x^2+12500*x)*log(x)^6+(3750*x*exp(3
)^2+(-6000*x^3-1500*x^2+37500*x)*exp(3)+2400*x^5+1200*x^4-29850*x^3-7500*x^2+93400*x)*log(x)^4+(2500*x*exp(3)^
3+(-6000*x^3-1500*x^2+37500*x)*exp(3)^2+(4800*x^5+2400*x^4-59700*x^3-15000*x^2+186800*x)*exp(3)-1280*x^7-960*x
^6+23760*x^5+11980*x^4-147940*x^3-37360*x^2+309000*x)*log(x)^2+625*x*exp(3)^4+(-2000*x^3-500*x^2+12500*x)*exp(
3)^3+(2400*x^5+1200*x^4-29850*x^3-7500*x^2+93400*x)*exp(3)^2+(-1280*x^7-960*x^6+23760*x^5+11980*x^4-147940*x^3
-37360*x^2+309000*x)*exp(3)+256*x^9+256*x^8-6304*x^7-4784*x^6+58577*x^5+29788*x^4-243464*x^3-61800*x^2+381924*
x),x, algorithm="fricas")

[Out]

-4/(16*x^4 + 25*log(x)^4 + 8*x^3 - 10*(4*x^2 + x - 5*e^3 - 25)*log(x)^2 - 199*x^2 - 10*(4*x^2 + x - 25)*e^3 -
50*x + 25*e^6 + 618)

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giac [B]  time = 135.63, size = 80, normalized size = 2.86 \begin {gather*} -\frac {8}{16 \, x^{4} - 40 \, x^{2} \log \relax (x)^{2} + 25 \, \log \relax (x)^{4} + 8 \, x^{3} - 40 \, x^{2} e^{3} - 10 \, x \log \relax (x)^{2} + 50 \, e^{3} \log \relax (x)^{2} - 199 \, x^{2} - 10 \, x e^{3} + 250 \, \log \relax (x)^{2} - 50 \, x + 25 \, e^{6} + 250 \, e^{3} + 618} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((400*log(x)^3+(-320*x^2-40*x)*log(x)^2+(400*exp(3)-320*x^2-80*x+2000)*log(x)+(-320*x^2-40*x)*exp(3)+
256*x^4+96*x^3-1592*x^2-200*x)/(625*x*log(x)^8+(2500*x*exp(3)-2000*x^3-500*x^2+12500*x)*log(x)^6+(3750*x*exp(3
)^2+(-6000*x^3-1500*x^2+37500*x)*exp(3)+2400*x^5+1200*x^4-29850*x^3-7500*x^2+93400*x)*log(x)^4+(2500*x*exp(3)^
3+(-6000*x^3-1500*x^2+37500*x)*exp(3)^2+(4800*x^5+2400*x^4-59700*x^3-15000*x^2+186800*x)*exp(3)-1280*x^7-960*x
^6+23760*x^5+11980*x^4-147940*x^3-37360*x^2+309000*x)*log(x)^2+625*x*exp(3)^4+(-2000*x^3-500*x^2+12500*x)*exp(
3)^3+(2400*x^5+1200*x^4-29850*x^3-7500*x^2+93400*x)*exp(3)^2+(-1280*x^7-960*x^6+23760*x^5+11980*x^4-147940*x^3
-37360*x^2+309000*x)*exp(3)+256*x^9+256*x^8-6304*x^7-4784*x^6+58577*x^5+29788*x^4-243464*x^3-61800*x^2+381924*
x),x, algorithm="giac")

[Out]

-8/(16*x^4 - 40*x^2*log(x)^2 + 25*log(x)^4 + 8*x^3 - 40*x^2*e^3 - 10*x*log(x)^2 + 50*e^3*log(x)^2 - 199*x^2 -
10*x*e^3 + 250*log(x)^2 - 50*x + 25*e^6 + 250*e^3 + 618)

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maple [B]  time = 0.07, size = 81, normalized size = 2.89

method result size
risch \(-\frac {4}{25 \ln \relax (x )^{4}-40 x^{2} \ln \relax (x )^{2}+16 x^{4}+50 \,{\mathrm e}^{3} \ln \relax (x )^{2}-10 x \ln \relax (x )^{2}-40 x^{2} {\mathrm e}^{3}+8 x^{3}+250 \ln \relax (x )^{2}+25 \,{\mathrm e}^{6}-10 x \,{\mathrm e}^{3}-199 x^{2}+250 \,{\mathrm e}^{3}-50 x +618}\) \(81\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((400*ln(x)^3+(-320*x^2-40*x)*ln(x)^2+(400*exp(3)-320*x^2-80*x+2000)*ln(x)+(-320*x^2-40*x)*exp(3)+256*x^4+9
6*x^3-1592*x^2-200*x)/(625*x*ln(x)^8+(2500*x*exp(3)-2000*x^3-500*x^2+12500*x)*ln(x)^6+(3750*x*exp(3)^2+(-6000*
x^3-1500*x^2+37500*x)*exp(3)+2400*x^5+1200*x^4-29850*x^3-7500*x^2+93400*x)*ln(x)^4+(2500*x*exp(3)^3+(-6000*x^3
-1500*x^2+37500*x)*exp(3)^2+(4800*x^5+2400*x^4-59700*x^3-15000*x^2+186800*x)*exp(3)-1280*x^7-960*x^6+23760*x^5
+11980*x^4-147940*x^3-37360*x^2+309000*x)*ln(x)^2+625*x*exp(3)^4+(-2000*x^3-500*x^2+12500*x)*exp(3)^3+(2400*x^
5+1200*x^4-29850*x^3-7500*x^2+93400*x)*exp(3)^2+(-1280*x^7-960*x^6+23760*x^5+11980*x^4-147940*x^3-37360*x^2+30
9000*x)*exp(3)+256*x^9+256*x^8-6304*x^7-4784*x^6+58577*x^5+29788*x^4-243464*x^3-61800*x^2+381924*x),x,method=_
RETURNVERBOSE)

[Out]

-4/(25*ln(x)^4-40*x^2*ln(x)^2+16*x^4+50*exp(3)*ln(x)^2-10*x*ln(x)^2-40*x^2*exp(3)+8*x^3+250*ln(x)^2+25*exp(6)-
10*x*exp(3)-199*x^2+250*exp(3)-50*x+618)

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maxima [B]  time = 0.91, size = 66, normalized size = 2.36 \begin {gather*} -\frac {4}{16 \, x^{4} + 25 \, \log \relax (x)^{4} + 8 \, x^{3} - x^{2} {\left (40 \, e^{3} + 199\right )} - 10 \, {\left (4 \, x^{2} + x - 5 \, e^{3} - 25\right )} \log \relax (x)^{2} - 10 \, x {\left (e^{3} + 5\right )} + 25 \, e^{6} + 250 \, e^{3} + 618} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((400*log(x)^3+(-320*x^2-40*x)*log(x)^2+(400*exp(3)-320*x^2-80*x+2000)*log(x)+(-320*x^2-40*x)*exp(3)+
256*x^4+96*x^3-1592*x^2-200*x)/(625*x*log(x)^8+(2500*x*exp(3)-2000*x^3-500*x^2+12500*x)*log(x)^6+(3750*x*exp(3
)^2+(-6000*x^3-1500*x^2+37500*x)*exp(3)+2400*x^5+1200*x^4-29850*x^3-7500*x^2+93400*x)*log(x)^4+(2500*x*exp(3)^
3+(-6000*x^3-1500*x^2+37500*x)*exp(3)^2+(4800*x^5+2400*x^4-59700*x^3-15000*x^2+186800*x)*exp(3)-1280*x^7-960*x
^6+23760*x^5+11980*x^4-147940*x^3-37360*x^2+309000*x)*log(x)^2+625*x*exp(3)^4+(-2000*x^3-500*x^2+12500*x)*exp(
3)^3+(2400*x^5+1200*x^4-29850*x^3-7500*x^2+93400*x)*exp(3)^2+(-1280*x^7-960*x^6+23760*x^5+11980*x^4-147940*x^3
-37360*x^2+309000*x)*exp(3)+256*x^9+256*x^8-6304*x^7-4784*x^6+58577*x^5+29788*x^4-243464*x^3-61800*x^2+381924*
x),x, algorithm="maxima")

[Out]

-4/(16*x^4 + 25*log(x)^4 + 8*x^3 - x^2*(40*e^3 + 199) - 10*(4*x^2 + x - 5*e^3 - 25)*log(x)^2 - 10*x*(e^3 + 5)
+ 25*e^6 + 250*e^3 + 618)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int -\frac {200\,x+{\ln \relax (x)}^2\,\left (320\,x^2+40\,x\right )+{\mathrm {e}}^3\,\left (320\,x^2+40\,x\right )-400\,{\ln \relax (x)}^3+\ln \relax (x)\,\left (320\,x^2+80\,x-400\,{\mathrm {e}}^3-2000\right )+1592\,x^2-96\,x^3-256\,x^4}{381924\,x+625\,x\,{\ln \relax (x)}^8+625\,x\,{\mathrm {e}}^{12}-{\mathrm {e}}^3\,\left (1280\,x^7+960\,x^6-23760\,x^5-11980\,x^4+147940\,x^3+37360\,x^2-309000\,x\right )+{\ln \relax (x)}^4\,\left (93400\,x+3750\,x\,{\mathrm {e}}^6-{\mathrm {e}}^3\,\left (6000\,x^3+1500\,x^2-37500\,x\right )-7500\,x^2-29850\,x^3+1200\,x^4+2400\,x^5\right )-{\mathrm {e}}^9\,\left (2000\,x^3+500\,x^2-12500\,x\right )+{\ln \relax (x)}^6\,\left (12500\,x+2500\,x\,{\mathrm {e}}^3-500\,x^2-2000\,x^3\right )+{\ln \relax (x)}^2\,\left (309000\,x+2500\,x\,{\mathrm {e}}^9-{\mathrm {e}}^6\,\left (6000\,x^3+1500\,x^2-37500\,x\right )+{\mathrm {e}}^3\,\left (4800\,x^5+2400\,x^4-59700\,x^3-15000\,x^2+186800\,x\right )-37360\,x^2-147940\,x^3+11980\,x^4+23760\,x^5-960\,x^6-1280\,x^7\right )+{\mathrm {e}}^6\,\left (2400\,x^5+1200\,x^4-29850\,x^3-7500\,x^2+93400\,x\right )-61800\,x^2-243464\,x^3+29788\,x^4+58577\,x^5-4784\,x^6-6304\,x^7+256\,x^8+256\,x^9} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(200*x + log(x)^2*(40*x + 320*x^2) + exp(3)*(40*x + 320*x^2) - 400*log(x)^3 + log(x)*(80*x - 400*exp(3) +
 320*x^2 - 2000) + 1592*x^2 - 96*x^3 - 256*x^4)/(381924*x + 625*x*log(x)^8 + 625*x*exp(12) - exp(3)*(37360*x^2
 - 309000*x + 147940*x^3 - 11980*x^4 - 23760*x^5 + 960*x^6 + 1280*x^7) + log(x)^4*(93400*x + 3750*x*exp(6) - e
xp(3)*(1500*x^2 - 37500*x + 6000*x^3) - 7500*x^2 - 29850*x^3 + 1200*x^4 + 2400*x^5) - exp(9)*(500*x^2 - 12500*
x + 2000*x^3) + log(x)^6*(12500*x + 2500*x*exp(3) - 500*x^2 - 2000*x^3) + log(x)^2*(309000*x + 2500*x*exp(9) -
 exp(6)*(1500*x^2 - 37500*x + 6000*x^3) + exp(3)*(186800*x - 15000*x^2 - 59700*x^3 + 2400*x^4 + 4800*x^5) - 37
360*x^2 - 147940*x^3 + 11980*x^4 + 23760*x^5 - 960*x^6 - 1280*x^7) + exp(6)*(93400*x - 7500*x^2 - 29850*x^3 +
1200*x^4 + 2400*x^5) - 61800*x^2 - 243464*x^3 + 29788*x^4 + 58577*x^5 - 4784*x^6 - 6304*x^7 + 256*x^8 + 256*x^
9),x)

[Out]

int(-(200*x + log(x)^2*(40*x + 320*x^2) + exp(3)*(40*x + 320*x^2) - 400*log(x)^3 + log(x)*(80*x - 400*exp(3) +
 320*x^2 - 2000) + 1592*x^2 - 96*x^3 - 256*x^4)/(381924*x + 625*x*log(x)^8 + 625*x*exp(12) - exp(3)*(37360*x^2
 - 309000*x + 147940*x^3 - 11980*x^4 - 23760*x^5 + 960*x^6 + 1280*x^7) + log(x)^4*(93400*x + 3750*x*exp(6) - e
xp(3)*(1500*x^2 - 37500*x + 6000*x^3) - 7500*x^2 - 29850*x^3 + 1200*x^4 + 2400*x^5) - exp(9)*(500*x^2 - 12500*
x + 2000*x^3) + log(x)^6*(12500*x + 2500*x*exp(3) - 500*x^2 - 2000*x^3) + log(x)^2*(309000*x + 2500*x*exp(9) -
 exp(6)*(1500*x^2 - 37500*x + 6000*x^3) + exp(3)*(186800*x - 15000*x^2 - 59700*x^3 + 2400*x^4 + 4800*x^5) - 37
360*x^2 - 147940*x^3 + 11980*x^4 + 23760*x^5 - 960*x^6 - 1280*x^7) + exp(6)*(93400*x - 7500*x^2 - 29850*x^3 +
1200*x^4 + 2400*x^5) - 61800*x^2 - 243464*x^3 + 29788*x^4 + 58577*x^5 - 4784*x^6 - 6304*x^7 + 256*x^8 + 256*x^
9), x)

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sympy [B]  time = 0.60, size = 75, normalized size = 2.68 \begin {gather*} - \frac {4}{16 x^{4} + 8 x^{3} - 40 x^{2} e^{3} - 199 x^{2} - 10 x e^{3} - 50 x + \left (- 40 x^{2} - 10 x + 250 + 50 e^{3}\right ) \log {\relax (x )}^{2} + 25 \log {\relax (x )}^{4} + 618 + 250 e^{3} + 25 e^{6}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((400*ln(x)**3+(-320*x**2-40*x)*ln(x)**2+(400*exp(3)-320*x**2-80*x+2000)*ln(x)+(-320*x**2-40*x)*exp(3
)+256*x**4+96*x**3-1592*x**2-200*x)/(625*x*ln(x)**8+(2500*x*exp(3)-2000*x**3-500*x**2+12500*x)*ln(x)**6+(3750*
x*exp(3)**2+(-6000*x**3-1500*x**2+37500*x)*exp(3)+2400*x**5+1200*x**4-29850*x**3-7500*x**2+93400*x)*ln(x)**4+(
2500*x*exp(3)**3+(-6000*x**3-1500*x**2+37500*x)*exp(3)**2+(4800*x**5+2400*x**4-59700*x**3-15000*x**2+186800*x)
*exp(3)-1280*x**7-960*x**6+23760*x**5+11980*x**4-147940*x**3-37360*x**2+309000*x)*ln(x)**2+625*x*exp(3)**4+(-2
000*x**3-500*x**2+12500*x)*exp(3)**3+(2400*x**5+1200*x**4-29850*x**3-7500*x**2+93400*x)*exp(3)**2+(-1280*x**7-
960*x**6+23760*x**5+11980*x**4-147940*x**3-37360*x**2+309000*x)*exp(3)+256*x**9+256*x**8-6304*x**7-4784*x**6+5
8577*x**5+29788*x**4-243464*x**3-61800*x**2+381924*x),x)

[Out]

-4/(16*x**4 + 8*x**3 - 40*x**2*exp(3) - 199*x**2 - 10*x*exp(3) - 50*x + (-40*x**2 - 10*x + 250 + 50*exp(3))*lo
g(x)**2 + 25*log(x)**4 + 618 + 250*exp(3) + 25*exp(6))

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