3.30.92 \(\int \frac {-625-625 x+250 e^2 x-25 e^4 x+(1000 x-200 e^2 x) \log (19)-400 x \log ^2(19)}{-15625+46875 x-46875 x^2+15625 x^3-30 e^{10} x^3+e^{12} x^3+e^2 (-18750 x+37500 x^2-18750 x^3)+e^6 (1500 x^2-2500 x^3)+e^8 (-75 x^2+375 x^3)+e^4 (1875 x-11250 x^2+9375 x^3)+(-75000 x+150000 x^2-75000 x^3-600 e^8 x^3+24 e^{10} x^3+e^4 (18000 x^2-30000 x^3)+e^6 (-1200 x^2+6000 x^3)+e^2 (15000 x-90000 x^2+75000 x^3)) \log (19)+(30000 x-180000 x^2+150000 x^3-4800 e^6 x^3+240 e^8 x^3+e^2 (72000 x^2-120000 x^3)+e^4 (-7200 x^2+36000 x^3)) \log ^2(19)+(96000 x^2-160000 x^3-19200 e^4 x^3+1280 e^6 x^3+e^2 (-19200 x^2+96000 x^3)) \log ^3(19)+(-19200 x^2+96000 x^3-38400 e^2 x^3+3840 e^4 x^3) \log ^4(19)+(-30720 x^3+6144 e^2 x^3) \log ^5(19)+4096 x^3 \log ^6(19)} \, dx\)

Optimal. Leaf size=22 \[ \frac {x}{\left (5-\frac {1}{5} x \left (-5+e^2+4 \log (19)\right )^2\right )^2} \]

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Rubi [B]  time = 0.22, antiderivative size = 71, normalized size of antiderivative = 3.23, number of steps used = 8, number of rules used = 2, integrand size = 389, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.005, Rules used = {6, 2074} \begin {gather*} \frac {625}{\left (5-e^2-4 \log (19)\right )^2 \left (25-x \left (5-e^2-4 \log (19)\right )^2\right )^2}-\frac {25}{\left (5-e^2-4 \log (19)\right )^2 \left (25-x \left (5-e^2-4 \log (19)\right )^2\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-625 - 625*x + 250*E^2*x - 25*E^4*x + (1000*x - 200*E^2*x)*Log[19] - 400*x*Log[19]^2)/(-15625 + 46875*x -
46875*x^2 + 15625*x^3 - 30*E^10*x^3 + E^12*x^3 + E^2*(-18750*x + 37500*x^2 - 18750*x^3) + E^6*(1500*x^2 - 250
0*x^3) + E^8*(-75*x^2 + 375*x^3) + E^4*(1875*x - 11250*x^2 + 9375*x^3) + (-75000*x + 150000*x^2 - 75000*x^3 -
600*E^8*x^3 + 24*E^10*x^3 + E^4*(18000*x^2 - 30000*x^3) + E^6*(-1200*x^2 + 6000*x^3) + E^2*(15000*x - 90000*x^
2 + 75000*x^3))*Log[19] + (30000*x - 180000*x^2 + 150000*x^3 - 4800*E^6*x^3 + 240*E^8*x^3 + E^2*(72000*x^2 - 1
20000*x^3) + E^4*(-7200*x^2 + 36000*x^3))*Log[19]^2 + (96000*x^2 - 160000*x^3 - 19200*E^4*x^3 + 1280*E^6*x^3 +
E^2*(-19200*x^2 + 96000*x^3))*Log[19]^3 + (-19200*x^2 + 96000*x^3 - 38400*E^2*x^3 + 3840*E^4*x^3)*Log[19]^4 +
(-30720*x^3 + 6144*E^2*x^3)*Log[19]^5 + 4096*x^3*Log[19]^6),x]

[Out]

625/((25 - x*(5 - E^2 - 4*Log[19])^2)^2*(5 - E^2 - 4*Log[19])^2) - 25/((25 - x*(5 - E^2 - 4*Log[19])^2)*(5 - E
^2 - 4*Log[19])^2)

Rule 6

Int[(u_.)*((w_.) + (a_.)*(v_) + (b_.)*(v_))^(p_.), x_Symbol] :> Int[u*((a + b)*v + w)^p, x] /; FreeQ[{a, b}, x
] &&  !FreeQ[v, x]

Rule 2074

Int[(P_)^(p_)*(Q_)^(q_.), x_Symbol] :> With[{PP = Factor[P]}, Int[ExpandIntegrand[PP^p*Q^q, x], x] /;  !SumQ[N
onfreeFactors[PP, x]]] /; FreeQ[q, x] && PolyQ[P, x] && PolyQ[Q, x] && IntegerQ[p] && NeQ[P, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-625-25 e^4 x+\left (-625+250 e^2\right ) x+\left (1000 x-200 e^2 x\right ) \log (19)-400 x \log ^2(19)}{-15625+46875 x-46875 x^2+15625 x^3-30 e^{10} x^3+e^{12} x^3+e^2 \left (-18750 x+37500 x^2-18750 x^3\right )+e^6 \left (1500 x^2-2500 x^3\right )+e^8 \left (-75 x^2+375 x^3\right )+e^4 \left (1875 x-11250 x^2+9375 x^3\right )+\left (-75000 x+150000 x^2-75000 x^3-600 e^8 x^3+24 e^{10} x^3+e^4 \left (18000 x^2-30000 x^3\right )+e^6 \left (-1200 x^2+6000 x^3\right )+e^2 \left (15000 x-90000 x^2+75000 x^3\right )\right ) \log (19)+\left (30000 x-180000 x^2+150000 x^3-4800 e^6 x^3+240 e^8 x^3+e^2 \left (72000 x^2-120000 x^3\right )+e^4 \left (-7200 x^2+36000 x^3\right )\right ) \log ^2(19)+\left (96000 x^2-160000 x^3-19200 e^4 x^3+1280 e^6 x^3+e^2 \left (-19200 x^2+96000 x^3\right )\right ) \log ^3(19)+\left (-19200 x^2+96000 x^3-38400 e^2 x^3+3840 e^4 x^3\right ) \log ^4(19)+\left (-30720 x^3+6144 e^2 x^3\right ) \log ^5(19)+4096 x^3 \log ^6(19)} \, dx\\ &=\int \frac {-625+\left (-625+250 e^2-25 e^4\right ) x+\left (1000 x-200 e^2 x\right ) \log (19)-400 x \log ^2(19)}{-15625+46875 x-46875 x^2+15625 x^3-30 e^{10} x^3+e^{12} x^3+e^2 \left (-18750 x+37500 x^2-18750 x^3\right )+e^6 \left (1500 x^2-2500 x^3\right )+e^8 \left (-75 x^2+375 x^3\right )+e^4 \left (1875 x-11250 x^2+9375 x^3\right )+\left (-75000 x+150000 x^2-75000 x^3-600 e^8 x^3+24 e^{10} x^3+e^4 \left (18000 x^2-30000 x^3\right )+e^6 \left (-1200 x^2+6000 x^3\right )+e^2 \left (15000 x-90000 x^2+75000 x^3\right )\right ) \log (19)+\left (30000 x-180000 x^2+150000 x^3-4800 e^6 x^3+240 e^8 x^3+e^2 \left (72000 x^2-120000 x^3\right )+e^4 \left (-7200 x^2+36000 x^3\right )\right ) \log ^2(19)+\left (96000 x^2-160000 x^3-19200 e^4 x^3+1280 e^6 x^3+e^2 \left (-19200 x^2+96000 x^3\right )\right ) \log ^3(19)+\left (-19200 x^2+96000 x^3-38400 e^2 x^3+3840 e^4 x^3\right ) \log ^4(19)+\left (-30720 x^3+6144 e^2 x^3\right ) \log ^5(19)+4096 x^3 \log ^6(19)} \, dx\\ &=\int \frac {-625+\left (1000 x-200 e^2 x\right ) \log (19)+x \left (-625+250 e^2-25 e^4-400 \log ^2(19)\right )}{-15625+46875 x-46875 x^2+15625 x^3-30 e^{10} x^3+e^{12} x^3+e^2 \left (-18750 x+37500 x^2-18750 x^3\right )+e^6 \left (1500 x^2-2500 x^3\right )+e^8 \left (-75 x^2+375 x^3\right )+e^4 \left (1875 x-11250 x^2+9375 x^3\right )+\left (-75000 x+150000 x^2-75000 x^3-600 e^8 x^3+24 e^{10} x^3+e^4 \left (18000 x^2-30000 x^3\right )+e^6 \left (-1200 x^2+6000 x^3\right )+e^2 \left (15000 x-90000 x^2+75000 x^3\right )\right ) \log (19)+\left (30000 x-180000 x^2+150000 x^3-4800 e^6 x^3+240 e^8 x^3+e^2 \left (72000 x^2-120000 x^3\right )+e^4 \left (-7200 x^2+36000 x^3\right )\right ) \log ^2(19)+\left (96000 x^2-160000 x^3-19200 e^4 x^3+1280 e^6 x^3+e^2 \left (-19200 x^2+96000 x^3\right )\right ) \log ^3(19)+\left (-19200 x^2+96000 x^3-38400 e^2 x^3+3840 e^4 x^3\right ) \log ^4(19)+\left (-30720 x^3+6144 e^2 x^3\right ) \log ^5(19)+4096 x^3 \log ^6(19)} \, dx\\ &=\int \frac {-625+\left (1000 x-200 e^2 x\right ) \log (19)+x \left (-625+250 e^2-25 e^4-400 \log ^2(19)\right )}{-15625+46875 x-46875 x^2+e^{12} x^3+\left (15625-30 e^{10}\right ) x^3+e^2 \left (-18750 x+37500 x^2-18750 x^3\right )+e^6 \left (1500 x^2-2500 x^3\right )+e^8 \left (-75 x^2+375 x^3\right )+e^4 \left (1875 x-11250 x^2+9375 x^3\right )+\left (-75000 x+150000 x^2-75000 x^3-600 e^8 x^3+24 e^{10} x^3+e^4 \left (18000 x^2-30000 x^3\right )+e^6 \left (-1200 x^2+6000 x^3\right )+e^2 \left (15000 x-90000 x^2+75000 x^3\right )\right ) \log (19)+\left (30000 x-180000 x^2+150000 x^3-4800 e^6 x^3+240 e^8 x^3+e^2 \left (72000 x^2-120000 x^3\right )+e^4 \left (-7200 x^2+36000 x^3\right )\right ) \log ^2(19)+\left (96000 x^2-160000 x^3-19200 e^4 x^3+1280 e^6 x^3+e^2 \left (-19200 x^2+96000 x^3\right )\right ) \log ^3(19)+\left (-19200 x^2+96000 x^3-38400 e^2 x^3+3840 e^4 x^3\right ) \log ^4(19)+\left (-30720 x^3+6144 e^2 x^3\right ) \log ^5(19)+4096 x^3 \log ^6(19)} \, dx\\ &=\int \frac {-625+\left (1000 x-200 e^2 x\right ) \log (19)+x \left (-625+250 e^2-25 e^4-400 \log ^2(19)\right )}{-15625+46875 x-46875 x^2+\left (15625-30 e^{10}+e^{12}\right ) x^3+e^2 \left (-18750 x+37500 x^2-18750 x^3\right )+e^6 \left (1500 x^2-2500 x^3\right )+e^8 \left (-75 x^2+375 x^3\right )+e^4 \left (1875 x-11250 x^2+9375 x^3\right )+\left (-75000 x+150000 x^2-75000 x^3-600 e^8 x^3+24 e^{10} x^3+e^4 \left (18000 x^2-30000 x^3\right )+e^6 \left (-1200 x^2+6000 x^3\right )+e^2 \left (15000 x-90000 x^2+75000 x^3\right )\right ) \log (19)+\left (30000 x-180000 x^2+150000 x^3-4800 e^6 x^3+240 e^8 x^3+e^2 \left (72000 x^2-120000 x^3\right )+e^4 \left (-7200 x^2+36000 x^3\right )\right ) \log ^2(19)+\left (96000 x^2-160000 x^3-19200 e^4 x^3+1280 e^6 x^3+e^2 \left (-19200 x^2+96000 x^3\right )\right ) \log ^3(19)+\left (-19200 x^2+96000 x^3-38400 e^2 x^3+3840 e^4 x^3\right ) \log ^4(19)+\left (-30720 x^3+6144 e^2 x^3\right ) \log ^5(19)+4096 x^3 \log ^6(19)} \, dx\\ &=\int \frac {-625+\left (1000 x-200 e^2 x\right ) \log (19)+x \left (-625+250 e^2-25 e^4-400 \log ^2(19)\right )}{-15625+46875 x-46875 x^2+e^2 \left (-18750 x+37500 x^2-18750 x^3\right )+e^6 \left (1500 x^2-2500 x^3\right )+e^8 \left (-75 x^2+375 x^3\right )+e^4 \left (1875 x-11250 x^2+9375 x^3\right )+\left (-75000 x+150000 x^2-75000 x^3-600 e^8 x^3+24 e^{10} x^3+e^4 \left (18000 x^2-30000 x^3\right )+e^6 \left (-1200 x^2+6000 x^3\right )+e^2 \left (15000 x-90000 x^2+75000 x^3\right )\right ) \log (19)+\left (30000 x-180000 x^2+150000 x^3-4800 e^6 x^3+240 e^8 x^3+e^2 \left (72000 x^2-120000 x^3\right )+e^4 \left (-7200 x^2+36000 x^3\right )\right ) \log ^2(19)+\left (96000 x^2-160000 x^3-19200 e^4 x^3+1280 e^6 x^3+e^2 \left (-19200 x^2+96000 x^3\right )\right ) \log ^3(19)+\left (-19200 x^2+96000 x^3-38400 e^2 x^3+3840 e^4 x^3\right ) \log ^4(19)+\left (-30720 x^3+6144 e^2 x^3\right ) \log ^5(19)+x^3 \left (15625-30 e^{10}+e^{12}+4096 \log ^6(19)\right )} \, dx\\ &=\int \left (\frac {1250}{\left (25-x \left (5-e^2-4 \log (19)\right )^2\right )^3}-\frac {25}{\left (25-x \left (5-e^2-4 \log (19)\right )^2\right )^2}\right ) \, dx\\ &=\frac {625}{\left (25-x \left (5-e^2-4 \log (19)\right )^2\right )^2 \left (5-e^2-4 \log (19)\right )^2}-\frac {25}{\left (25-x \left (5-e^2-4 \log (19)\right )^2\right ) \left (5-e^2-4 \log (19)\right )^2}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.03, size = 20, normalized size = 0.91 \begin {gather*} \frac {25 x}{\left (-25+x \left (-5+e^2+4 \log (19)\right )^2\right )^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-625 - 625*x + 250*E^2*x - 25*E^4*x + (1000*x - 200*E^2*x)*Log[19] - 400*x*Log[19]^2)/(-15625 + 468
75*x - 46875*x^2 + 15625*x^3 - 30*E^10*x^3 + E^12*x^3 + E^2*(-18750*x + 37500*x^2 - 18750*x^3) + E^6*(1500*x^2
- 2500*x^3) + E^8*(-75*x^2 + 375*x^3) + E^4*(1875*x - 11250*x^2 + 9375*x^3) + (-75000*x + 150000*x^2 - 75000*
x^3 - 600*E^8*x^3 + 24*E^10*x^3 + E^4*(18000*x^2 - 30000*x^3) + E^6*(-1200*x^2 + 6000*x^3) + E^2*(15000*x - 90
000*x^2 + 75000*x^3))*Log[19] + (30000*x - 180000*x^2 + 150000*x^3 - 4800*E^6*x^3 + 240*E^8*x^3 + E^2*(72000*x
^2 - 120000*x^3) + E^4*(-7200*x^2 + 36000*x^3))*Log[19]^2 + (96000*x^2 - 160000*x^3 - 19200*E^4*x^3 + 1280*E^6
*x^3 + E^2*(-19200*x^2 + 96000*x^3))*Log[19]^3 + (-19200*x^2 + 96000*x^3 - 38400*E^2*x^3 + 3840*E^4*x^3)*Log[1
9]^4 + (-30720*x^3 + 6144*E^2*x^3)*Log[19]^5 + 4096*x^3*Log[19]^6),x]

[Out]

(25*x)/(-25 + x*(-5 + E^2 + 4*Log[19])^2)^2

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fricas [B]  time = 0.84, size = 147, normalized size = 6.68 \begin {gather*} \frac {25 \, x}{256 \, x^{2} \log \left (19\right )^{4} + 256 \, {\left (x^{2} e^{2} - 5 \, x^{2}\right )} \log \left (19\right )^{3} + x^{2} e^{8} - 20 \, x^{2} e^{6} + 32 \, {\left (3 \, x^{2} e^{4} - 30 \, x^{2} e^{2} + 75 \, x^{2} - 25 \, x\right )} \log \left (19\right )^{2} + 625 \, x^{2} + 50 \, {\left (3 \, x^{2} - x\right )} e^{4} - 500 \, {\left (x^{2} - x\right )} e^{2} + 16 \, {\left (x^{2} e^{6} - 15 \, x^{2} e^{4} - 125 \, x^{2} + 25 \, {\left (3 \, x^{2} - x\right )} e^{2} + 125 \, x\right )} \log \left (19\right ) - 1250 \, x + 625} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-400*x*log(19)^2+(-200*exp(2)*x+1000*x)*log(19)-25*x*exp(2)^2+250*exp(2)*x-625*x-625)/(4096*x^3*log
(19)^6+(6144*x^3*exp(2)-30720*x^3)*log(19)^5+(3840*x^3*exp(2)^2-38400*x^3*exp(2)+96000*x^3-19200*x^2)*log(19)^
4+(1280*x^3*exp(2)^3-19200*x^3*exp(2)^2+(96000*x^3-19200*x^2)*exp(2)-160000*x^3+96000*x^2)*log(19)^3+(240*x^3*
exp(2)^4-4800*x^3*exp(2)^3+(36000*x^3-7200*x^2)*exp(2)^2+(-120000*x^3+72000*x^2)*exp(2)+150000*x^3-180000*x^2+
30000*x)*log(19)^2+(24*x^3*exp(2)^5-600*x^3*exp(2)^4+(6000*x^3-1200*x^2)*exp(2)^3+(-30000*x^3+18000*x^2)*exp(2
)^2+(75000*x^3-90000*x^2+15000*x)*exp(2)-75000*x^3+150000*x^2-75000*x)*log(19)+x^3*exp(2)^6-30*x^3*exp(2)^5+(3
75*x^3-75*x^2)*exp(2)^4+(-2500*x^3+1500*x^2)*exp(2)^3+(9375*x^3-11250*x^2+1875*x)*exp(2)^2+(-18750*x^3+37500*x
^2-18750*x)*exp(2)+15625*x^3-46875*x^2+46875*x-15625),x, algorithm="fricas")

[Out]

25*x/(256*x^2*log(19)^4 + 256*(x^2*e^2 - 5*x^2)*log(19)^3 + x^2*e^8 - 20*x^2*e^6 + 32*(3*x^2*e^4 - 30*x^2*e^2
+ 75*x^2 - 25*x)*log(19)^2 + 625*x^2 + 50*(3*x^2 - x)*e^4 - 500*(x^2 - x)*e^2 + 16*(x^2*e^6 - 15*x^2*e^4 - 125
*x^2 + 25*(3*x^2 - x)*e^2 + 125*x)*log(19) - 1250*x + 625)

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giac [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-400*x*log(19)^2+(-200*exp(2)*x+1000*x)*log(19)-25*x*exp(2)^2+250*exp(2)*x-625*x-625)/(4096*x^3*log
(19)^6+(6144*x^3*exp(2)-30720*x^3)*log(19)^5+(3840*x^3*exp(2)^2-38400*x^3*exp(2)+96000*x^3-19200*x^2)*log(19)^
4+(1280*x^3*exp(2)^3-19200*x^3*exp(2)^2+(96000*x^3-19200*x^2)*exp(2)-160000*x^3+96000*x^2)*log(19)^3+(240*x^3*
exp(2)^4-4800*x^3*exp(2)^3+(36000*x^3-7200*x^2)*exp(2)^2+(-120000*x^3+72000*x^2)*exp(2)+150000*x^3-180000*x^2+
30000*x)*log(19)^2+(24*x^3*exp(2)^5-600*x^3*exp(2)^4+(6000*x^3-1200*x^2)*exp(2)^3+(-30000*x^3+18000*x^2)*exp(2
)^2+(75000*x^3-90000*x^2+15000*x)*exp(2)-75000*x^3+150000*x^2-75000*x)*log(19)+x^3*exp(2)^6-30*x^3*exp(2)^5+(3
75*x^3-75*x^2)*exp(2)^4+(-2500*x^3+1500*x^2)*exp(2)^3+(9375*x^3-11250*x^2+1875*x)*exp(2)^2+(-18750*x^3+37500*x
^2-18750*x)*exp(2)+15625*x^3-46875*x^2+46875*x-15625),x, algorithm="giac")

[Out]

Timed out

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maple [B]  time = 0.41, size = 41, normalized size = 1.86

method	result	size
norman	\(\frac {25 x}{\left (x \,{\mathrm e}^{4}+8 \,{\mathrm e}^{2} \ln \left (19\right ) x +16 x \ln \left (19\right )^{2}-10 \,{\mathrm e}^{2} x -40 \ln \left (19\right ) x +25 x -25\right )^{2}}\)	\(41\)
risch	\(\frac {25 x}{x^{2} {\mathrm e}^{8}+16 \,{\mathrm e}^{6} \ln \left (19\right ) x^{2}+96 \,{\mathrm e}^{4} \ln \left (19\right )^{2} x^{2}+256 \,{\mathrm e}^{2} \ln \left (19\right )^{3} x^{2}+256 \ln \left (19\right )^{4} x^{2}-20 x^{2} {\mathrm e}^{6}-240 \,{\mathrm e}^{4} \ln \left (19\right ) x^{2}-960 \,{\mathrm e}^{2} \ln \left (19\right )^{2} x^{2}-1280 \ln \left (19\right )^{3} x^{2}+150 x^{2} {\mathrm e}^{4}+1200 \,{\mathrm e}^{2} \ln \left (19\right ) x^{2}+2400 \ln \left (19\right )^{2} x^{2}-50 x \,{\mathrm e}^{4}-400 \,{\mathrm e}^{2} \ln \left (19\right ) x -500 x^{2} {\mathrm e}^{2}-800 x \ln \left (19\right )^{2}-2000 \ln \left (19\right ) x^{2}+500 \,{\mathrm e}^{2} x +2000 \ln \left (19\right ) x +625 x^{2}-1250 x +625}\)	\(166\)
gosper	\(\frac {25 x}{x^{2} {\mathrm e}^{8}+16 \,{\mathrm e}^{6} \ln \left (19\right ) x^{2}+96 \,{\mathrm e}^{4} \ln \left (19\right )^{2} x^{2}+256 \,{\mathrm e}^{2} \ln \left (19\right )^{3} x^{2}+256 \ln \left (19\right )^{4} x^{2}-20 x^{2} {\mathrm e}^{6}-240 \,{\mathrm e}^{4} \ln \left (19\right ) x^{2}-960 \,{\mathrm e}^{2} \ln \left (19\right )^{2} x^{2}-1280 \ln \left (19\right )^{3} x^{2}+150 x^{2} {\mathrm e}^{4}+1200 \,{\mathrm e}^{2} \ln \left (19\right ) x^{2}+2400 \ln \left (19\right )^{2} x^{2}-50 x \,{\mathrm e}^{4}-400 \,{\mathrm e}^{2} \ln \left (19\right ) x -500 x^{2} {\mathrm e}^{2}-800 x \ln \left (19\right )^{2}-2000 \ln \left (19\right ) x^{2}+500 \,{\mathrm e}^{2} x +2000 \ln \left (19\right ) x +625 x^{2}-1250 x +625}\)	\(180\)
default	\(\frac {25 \left (\munderset {\textit {\_R} =\RootOf \left (-15625+\left (15625+75000 \ln \left (19\right ) {\mathrm e}^{2}+375 \,{\mathrm e}^{8}-30 \,{\mathrm e}^{10}-2500 \,{\mathrm e}^{6}+9375 \,{\mathrm e}^{4}-18750 \,{\mathrm e}^{2}-75000 \ln \left (19\right )+{\mathrm e}^{12}+24 \,{\mathrm e}^{10} \ln \left (19\right )+240 \,{\mathrm e}^{8} \ln \left (19\right )^{2}+1280 \,{\mathrm e}^{6} \ln \left (19\right )^{3}+3840 \,{\mathrm e}^{4} \ln \left (19\right )^{4}-600 \,{\mathrm e}^{8} \ln \left (19\right )-4800 \,{\mathrm e}^{6} \ln \left (19\right )^{2}-19200 \,{\mathrm e}^{4} \ln \left (19\right )^{3}+6144 \,{\mathrm e}^{2} \ln \left (19\right )^{5}-38400 \,{\mathrm e}^{2} \ln \left (19\right )^{4}+96000 \,{\mathrm e}^{2} \ln \left (19\right )^{3}-120000 \,{\mathrm e}^{2} \ln \left (19\right )^{2}+6000 \,{\mathrm e}^{6} \ln \left (19\right )+36000 \,{\mathrm e}^{4} \ln \left (19\right )^{2}-30000 \,{\mathrm e}^{4} \ln \left (19\right )-160000 \ln \left (19\right )^{3}+150000 \ln \left (19\right )^{2}+4096 \ln \left (19\right )^{6}-30720 \ln \left (19\right )^{5}+96000 \ln \left (19\right )^{4}\right ) \textit {\_Z}^{3}+\left (1500 \,{\mathrm e}^{6}-75 \,{\mathrm e}^{8}-46875-11250 \,{\mathrm e}^{4}+37500 \,{\mathrm e}^{2}-19200 \ln \left (19\right )^{4}+96000 \ln \left (19\right )^{3}-180000 \ln \left (19\right )^{2}+150000 \ln \left (19\right )-1200 \,{\mathrm e}^{6} \ln \left (19\right )-7200 \,{\mathrm e}^{4} \ln \left (19\right )^{2}+18000 \,{\mathrm e}^{4} \ln \left (19\right )-19200 \,{\mathrm e}^{2} \ln \left (19\right )^{3}+72000 \,{\mathrm e}^{2} \ln \left (19\right )^{2}-90000 \ln \left (19\right ) {\mathrm e}^{2}\right ) \textit {\_Z}^{2}+\left (46875-18750 \,{\mathrm e}^{2}-75000 \ln \left (19\right )+1875 \,{\mathrm e}^{4}+30000 \ln \left (19\right )^{2}+15000 \ln \left (19\right ) {\mathrm e}^{2}\right ) \textit {\_Z} \right )}{\sum }\frac {\left (-\textit {\_R} \,{\mathrm e}^{4}-8 \,{\mathrm e}^{2} \ln \left (19\right ) \textit {\_R} -16 \textit {\_R} \ln \left (19\right )^{2}+10 \,{\mathrm e}^{2} \textit {\_R} +40 \ln \left (19\right ) \textit {\_R} -25 \textit {\_R} -25\right ) \ln \left (x -\textit {\_R} \right )}{15625-31250 \textit {\_R} +5000 \ln \left (19\right ) {\mathrm e}^{2}+625 \,{\mathrm e}^{4}-6250 \,{\mathrm e}^{2}-2500 \textit {\_R}^{2} {\mathrm e}^{6}-25000 \ln \left (19\right )+15625 \textit {\_R}^{2}-7500 \textit {\_R} \,{\mathrm e}^{4}-120000 \textit {\_R} \ln \left (19\right )^{2}+25000 \,{\mathrm e}^{2} \textit {\_R} +100000 \ln \left (19\right ) \textit {\_R} -12800 \ln \left (19\right )^{4} \textit {\_R} +64000 \ln \left (19\right )^{3} \textit {\_R} -50 \textit {\_R} \,{\mathrm e}^{8}+375 \textit {\_R}^{2} {\mathrm e}^{8}+9375 \textit {\_R}^{2} {\mathrm e}^{4}+1000 \textit {\_R} \,{\mathrm e}^{6}-18750 \textit {\_R}^{2} {\mathrm e}^{2}-30 \textit {\_R}^{2} {\mathrm e}^{10}+96000 \ln \left (19\right )^{4} \textit {\_R}^{2}-160000 \ln \left (19\right )^{3} \textit {\_R}^{2}+150000 \ln \left (19\right )^{2} \textit {\_R}^{2}-75000 \ln \left (19\right ) \textit {\_R}^{2}-30720 \ln \left (19\right )^{5} \textit {\_R}^{2}+{\mathrm e}^{12} \textit {\_R}^{2}+4096 \textit {\_R}^{2} \ln \left (19\right )^{6}+10000 \ln \left (19\right )^{2}-60000 \,{\mathrm e}^{2} \ln \left (19\right ) \textit {\_R} +6000 \,{\mathrm e}^{6} \ln \left (19\right ) \textit {\_R}^{2}+36000 \,{\mathrm e}^{4} \ln \left (19\right )^{2} \textit {\_R}^{2}-30000 \,{\mathrm e}^{4} \ln \left (19\right ) \textit {\_R}^{2}-12800 \,{\mathrm e}^{2} \ln \left (19\right )^{3} \textit {\_R} +48000 \,{\mathrm e}^{2} \ln \left (19\right )^{2} \textit {\_R} +96000 \,{\mathrm e}^{2} \ln \left (19\right )^{3} \textit {\_R}^{2}-120000 \,{\mathrm e}^{2} \ln \left (19\right )^{2} \textit {\_R}^{2}+75000 \,{\mathrm e}^{2} \ln \left (19\right ) \textit {\_R}^{2}+6144 \,{\mathrm e}^{2} \ln \left (19\right )^{5} \textit {\_R}^{2}-38400 \,{\mathrm e}^{2} \ln \left (19\right )^{4} \textit {\_R}^{2}+24 \,{\mathrm e}^{10} \ln \left (19\right ) \textit {\_R}^{2}+240 \,{\mathrm e}^{8} \ln \left (19\right )^{2} \textit {\_R}^{2}+1280 \,{\mathrm e}^{6} \ln \left (19\right )^{3} \textit {\_R}^{2}+3840 \,{\mathrm e}^{4} \ln \left (19\right )^{4} \textit {\_R}^{2}-600 \,{\mathrm e}^{8} \ln \left (19\right ) \textit {\_R}^{2}-4800 \,{\mathrm e}^{6} \ln \left (19\right )^{2} \textit {\_R}^{2}-19200 \,{\mathrm e}^{4} \ln \left (19\right )^{3} \textit {\_R}^{2}-800 \,{\mathrm e}^{6} \ln \left (19\right ) \textit {\_R} -4800 \,{\mathrm e}^{4} \ln \left (19\right )^{2} \textit {\_R} +12000 \,{\mathrm e}^{4} \ln \left (19\right ) \textit {\_R}}\right )}{3}\)	\(714\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-400*x*ln(19)^2+(-200*exp(2)*x+1000*x)*ln(19)-25*x*exp(2)^2+250*exp(2)*x-625*x-625)/(4096*x^3*ln(19)^6+(6
144*x^3*exp(2)-30720*x^3)*ln(19)^5+(3840*x^3*exp(2)^2-38400*x^3*exp(2)+96000*x^3-19200*x^2)*ln(19)^4+(1280*x^3
*exp(2)^3-19200*x^3*exp(2)^2+(96000*x^3-19200*x^2)*exp(2)-160000*x^3+96000*x^2)*ln(19)^3+(240*x^3*exp(2)^4-480
0*x^3*exp(2)^3+(36000*x^3-7200*x^2)*exp(2)^2+(-120000*x^3+72000*x^2)*exp(2)+150000*x^3-180000*x^2+30000*x)*ln(
19)^2+(24*x^3*exp(2)^5-600*x^3*exp(2)^4+(6000*x^3-1200*x^2)*exp(2)^3+(-30000*x^3+18000*x^2)*exp(2)^2+(75000*x^
3-90000*x^2+15000*x)*exp(2)-75000*x^3+150000*x^2-75000*x)*ln(19)+x^3*exp(2)^6-30*x^3*exp(2)^5+(375*x^3-75*x^2)
*exp(2)^4+(-2500*x^3+1500*x^2)*exp(2)^3+(9375*x^3-11250*x^2+1875*x)*exp(2)^2+(-18750*x^3+37500*x^2-18750*x)*ex
p(2)+15625*x^3-46875*x^2+46875*x-15625),x,method=_RETURNVERBOSE)

[Out]

25*x/(x*exp(2)^2+8*exp(2)*ln(19)*x+16*x*ln(19)^2-10*exp(2)*x-40*ln(19)*x+25*x-25)^2

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maxima [B]  time = 0.66, size = 98, normalized size = 4.45 \begin {gather*} \frac {25 \, x}{{\left (256 \, {\left (e^{2} - 5\right )} \log \left (19\right )^{3} + 256 \, \log \left (19\right )^{4} + 96 \, {\left (e^{4} - 10 \, e^{2} + 25\right )} \log \left (19\right )^{2} + 16 \, {\left (e^{6} - 15 \, e^{4} + 75 \, e^{2} - 125\right )} \log \left (19\right ) + e^{8} - 20 \, e^{6} + 150 \, e^{4} - 500 \, e^{2} + 625\right )} x^{2} - 50 \, {\left (8 \, {\left (e^{2} - 5\right )} \log \left (19\right ) + 16 \, \log \left (19\right )^{2} + e^{4} - 10 \, e^{2} + 25\right )} x + 625} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-400*x*log(19)^2+(-200*exp(2)*x+1000*x)*log(19)-25*x*exp(2)^2+250*exp(2)*x-625*x-625)/(4096*x^3*log
(19)^6+(6144*x^3*exp(2)-30720*x^3)*log(19)^5+(3840*x^3*exp(2)^2-38400*x^3*exp(2)+96000*x^3-19200*x^2)*log(19)^
4+(1280*x^3*exp(2)^3-19200*x^3*exp(2)^2+(96000*x^3-19200*x^2)*exp(2)-160000*x^3+96000*x^2)*log(19)^3+(240*x^3*
exp(2)^4-4800*x^3*exp(2)^3+(36000*x^3-7200*x^2)*exp(2)^2+(-120000*x^3+72000*x^2)*exp(2)+150000*x^3-180000*x^2+
30000*x)*log(19)^2+(24*x^3*exp(2)^5-600*x^3*exp(2)^4+(6000*x^3-1200*x^2)*exp(2)^3+(-30000*x^3+18000*x^2)*exp(2
)^2+(75000*x^3-90000*x^2+15000*x)*exp(2)-75000*x^3+150000*x^2-75000*x)*log(19)+x^3*exp(2)^6-30*x^3*exp(2)^5+(3
75*x^3-75*x^2)*exp(2)^4+(-2500*x^3+1500*x^2)*exp(2)^3+(9375*x^3-11250*x^2+1875*x)*exp(2)^2+(-18750*x^3+37500*x
^2-18750*x)*exp(2)+15625*x^3-46875*x^2+46875*x-15625),x, algorithm="maxima")

[Out]

25*x/((256*(e^2 - 5)*log(19)^3 + 256*log(19)^4 + 96*(e^4 - 10*e^2 + 25)*log(19)^2 + 16*(e^6 - 15*e^4 + 75*e^2
- 125)*log(19) + e^8 - 20*e^6 + 150*e^4 - 500*e^2 + 625)*x^2 - 50*(8*(e^2 - 5)*log(19) + 16*log(19)^2 + e^4 -
10*e^2 + 25)*x + 625)

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mupad [B]  time = 2.35, size = 120, normalized size = 5.45 \begin {gather*} \frac {25\,x}{\left (150\,{\mathrm {e}}^4-500\,{\mathrm {e}}^2-20\,{\mathrm {e}}^6+{\mathrm {e}}^8-2000\,\ln \left (19\right )+1200\,{\mathrm {e}}^2\,\ln \left (19\right )-240\,{\mathrm {e}}^4\,\ln \left (19\right )+16\,{\mathrm {e}}^6\,\ln \left (19\right )-960\,{\mathrm {e}}^2\,{\ln \left (19\right )}^2+256\,{\mathrm {e}}^2\,{\ln \left (19\right )}^3+96\,{\mathrm {e}}^4\,{\ln \left (19\right )}^2+2400\,{\ln \left (19\right )}^2-1280\,{\ln \left (19\right )}^3+256\,{\ln \left (19\right )}^4+625\right )\,x^2+\left (500\,{\mathrm {e}}^2-50\,{\mathrm {e}}^4+2000\,\ln \left (19\right )-400\,{\mathrm {e}}^2\,\ln \left (19\right )-800\,{\ln \left (19\right )}^2-1250\right )\,x+625} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(625*x - 250*x*exp(2) + 25*x*exp(4) - log(19)*(1000*x - 200*x*exp(2)) + 400*x*log(19)^2 + 625)/(46875*x +
4096*x^3*log(19)^6 + log(19)^2*(30000*x - exp(4)*(7200*x^2 - 36000*x^3) + exp(2)*(72000*x^2 - 120000*x^3) - 4
800*x^3*exp(6) + 240*x^3*exp(8) - 180000*x^2 + 150000*x^3) - log(19)^4*(38400*x^3*exp(2) - 3840*x^3*exp(4) + 1
9200*x^2 - 96000*x^3) - log(19)*(75000*x - exp(2)*(15000*x - 90000*x^2 + 75000*x^3) + exp(6)*(1200*x^2 - 6000*
x^3) - exp(4)*(18000*x^2 - 30000*x^3) + 600*x^3*exp(8) - 24*x^3*exp(10) - 150000*x^2 + 75000*x^3) + log(19)^5*
(6144*x^3*exp(2) - 30720*x^3) + exp(4)*(1875*x - 11250*x^2 + 9375*x^3) - exp(2)*(18750*x - 37500*x^2 + 18750*x
^3) - exp(8)*(75*x^2 - 375*x^3) + exp(6)*(1500*x^2 - 2500*x^3) - 30*x^3*exp(10) + x^3*exp(12) - log(19)^3*(exp
(2)*(19200*x^2 - 96000*x^3) + 19200*x^3*exp(4) - 1280*x^3*exp(6) - 96000*x^2 + 160000*x^3) - 46875*x^2 + 15625
*x^3 - 15625),x)

[Out]

(25*x)/(x^2*(150*exp(4) - 500*exp(2) - 20*exp(6) + exp(8) - 2000*log(19) + 1200*exp(2)*log(19) - 240*exp(4)*lo
g(19) + 16*exp(6)*log(19) - 960*exp(2)*log(19)^2 + 256*exp(2)*log(19)^3 + 96*exp(4)*log(19)^2 + 2400*log(19)^2
- 1280*log(19)^3 + 256*log(19)^4 + 625) - x*(50*exp(4) - 500*exp(2) - 2000*log(19) + 400*exp(2)*log(19) + 800
*log(19)^2 + 1250) + 625)

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sympy [B]  time = 5.82, size = 143, normalized size = 6.50 \begin {gather*} \frac {25 x}{x^{2} \left (- 960 e^{2} \log {\left (19 \right )}^{2} - 240 e^{4} \log {\left (19 \right )} - 1280 \log {\left (19 \right )}^{3} - 20 e^{6} - 2000 \log {\left (19 \right )} - 500 e^{2} + 625 + e^{8} + 150 e^{4} + 16 e^{6} \log {\left (19 \right )} + 256 \log {\left (19 \right )}^{4} + 2400 \log {\left (19 \right )}^{2} + 1200 e^{2} \log {\left (19 \right )} + 96 e^{4} \log {\left (19 \right )}^{2} + 256 e^{2} \log {\left (19 \right )}^{3}\right ) + x \left (- 400 e^{2} \log {\left (19 \right )} - 800 \log {\left (19 \right )}^{2} - 50 e^{4} - 1250 + 500 e^{2} + 2000 \log {\left (19 \right )}\right ) + 625} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-400*x*ln(19)**2+(-200*exp(2)*x+1000*x)*ln(19)-25*x*exp(2)**2+250*exp(2)*x-625*x-625)/(4096*x**3*ln
(19)**6+(6144*x**3*exp(2)-30720*x**3)*ln(19)**5+(3840*x**3*exp(2)**2-38400*x**3*exp(2)+96000*x**3-19200*x**2)*
ln(19)**4+(1280*x**3*exp(2)**3-19200*x**3*exp(2)**2+(96000*x**3-19200*x**2)*exp(2)-160000*x**3+96000*x**2)*ln(
19)**3+(240*x**3*exp(2)**4-4800*x**3*exp(2)**3+(36000*x**3-7200*x**2)*exp(2)**2+(-120000*x**3+72000*x**2)*exp(
2)+150000*x**3-180000*x**2+30000*x)*ln(19)**2+(24*x**3*exp(2)**5-600*x**3*exp(2)**4+(6000*x**3-1200*x**2)*exp(
2)**3+(-30000*x**3+18000*x**2)*exp(2)**2+(75000*x**3-90000*x**2+15000*x)*exp(2)-75000*x**3+150000*x**2-75000*x
)*ln(19)+x**3*exp(2)**6-30*x**3*exp(2)**5+(375*x**3-75*x**2)*exp(2)**4+(-2500*x**3+1500*x**2)*exp(2)**3+(9375*
x**3-11250*x**2+1875*x)*exp(2)**2+(-18750*x**3+37500*x**2-18750*x)*exp(2)+15625*x**3-46875*x**2+46875*x-15625)
,x)

[Out]

25*x/(x**2*(-960*exp(2)*log(19)**2 - 240*exp(4)*log(19) - 1280*log(19)**3 - 20*exp(6) - 2000*log(19) - 500*exp
(2) + 625 + exp(8) + 150*exp(4) + 16*exp(6)*log(19) + 256*log(19)**4 + 2400*log(19)**2 + 1200*exp(2)*log(19) +
96*exp(4)*log(19)**2 + 256*exp(2)*log(19)**3) + x*(-400*exp(2)*log(19) - 800*log(19)**2 - 50*exp(4) - 1250 +
500*exp(2) + 2000*log(19)) + 625)

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