\(\int \frac {390625 x-1562500 x^2-100000000 x^4+400000000 x^5+e^{8 e} (-x^4+4 x^5)+e^{6 e} (-400 x^4+1600 x^5)+e^{4 e} (-60000 x^4+240000 x^5)+e^{2 e} (-4000000 x^4+16000000 x^5)+(781250 x-4687500 x^2-500000000 x^4+2400000000 x^5+e^{8 e} (-5 x^4+24 x^5)+e^{6 e} (-2000 x^4+9600 x^5)+e^{4 e} (-300000 x^4+1440000 x^5)+e^{2 e} (-20000000 x^4+96000000 x^5)) \log (x)}{390625} \, dx\) [3374]

Optimal result

Integrand size = 181, antiderivative size = 33 \[ \int \frac {390625 x-1562500 x^2-100000000 x^4+400000000 x^5+e^{8 e} \left (-x^4+4 x^5\right )+e^{6 e} \left (-400 x^4+1600 x^5\right )+e^{4 e} \left (-60000 x^4+240000 x^5\right )+e^{2 e} \left (-4000000 x^4+16000000 x^5\right )+\left (781250 x-4687500 x^2-500000000 x^4+2400000000 x^5+e^{8 e} \left (-5 x^4+24 x^5\right )+e^{6 e} \left (-2000 x^4+9600 x^5\right )+e^{4 e} \left (-300000 x^4+1440000 x^5\right )+e^{2 e} \left (-20000000 x^4+96000000 x^5\right )\right ) \log (x)}{390625} \, dx=\left (-x+4 x^2\right ) \left (-x+\left (4+\frac {e^{2 e}}{25}\right )^4 x^4\right ) \log (x) \]

[Out]

(4*x^2-x)*ln(x)*(x^4*(1/25*exp(exp(1))^2+4)^4-x)

Rubi [B] (verified)

Leaf count is larger than twice the leaf count of optimal. \(192\) vs. \(2(33)=66\).

Time = 0.12 (sec) , antiderivative size = 192, normalized size of antiderivative = 5.82, number of steps used = 12, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.017, Rules used = {12, 2403, 2341} \[ \int \frac {390625 x-1562500 x^2-100000000 x^4+400000000 x^5+e^{8 e} \left (-x^4+4 x^5\right )+e^{6 e} \left (-400 x^4+1600 x^5\right )+e^{4 e} \left (-60000 x^4+240000 x^5\right )+e^{2 e} \left (-4000000 x^4+16000000 x^5\right )+\left (781250 x-4687500 x^2-500000000 x^4+2400000000 x^5+e^{8 e} \left (-5 x^4+24 x^5\right )+e^{6 e} \left (-2000 x^4+9600 x^5\right )+e^{4 e} \left (-300000 x^4+1440000 x^5\right )+e^{2 e} \left (-20000000 x^4+96000000 x^5\right )\right ) \log (x)}{390625} \, dx=-\frac {2 \left (100+e^{2 e}\right )^4 x^6}{1171875}+\frac {2 e^{8 e} x^6}{1171875}+\frac {32 e^{6 e} x^6}{46875}+\frac {64}{625} e^{4 e} x^6+\frac {512}{75} e^{2 e} x^6+\frac {512 x^6}{3}+\frac {4 \left (100+e^{2 e}\right )^4 x^6 \log (x)}{390625}+\frac {\left (100+e^{2 e}\right )^4 x^5}{1953125}-\frac {e^{8 e} x^5}{1953125}-\frac {16 e^{6 e} x^5}{78125}-\frac {96 e^{4 e} x^5}{3125}-\frac {256}{125} e^{2 e} x^5-\frac {256 x^5}{5}-\frac {\left (100+e^{2 e}\right )^4 x^5 \log (x)}{390625}-4 x^3 \log (x)+x^2 \log (x) \]

[In]

Int[(390625*x - 1562500*x^2 - 100000000*x^4 + 400000000*x^5 + E^(8*E)*(-x^4 + 4*x^5) + E^(6*E)*(-400*x^4 + 160
0*x^5) + E^(4*E)*(-60000*x^4 + 240000*x^5) + E^(2*E)*(-4000000*x^4 + 16000000*x^5) + (781250*x - 4687500*x^2 -
500000000*x^4 + 2400000000*x^5 + E^(8*E)*(-5*x^4 + 24*x^5) + E^(6*E)*(-2000*x^4 + 9600*x^5) + E^(4*E)*(-30000
0*x^4 + 1440000*x^5) + E^(2*E)*(-20000000*x^4 + 96000000*x^5))*Log[x])/390625,x]

[Out]

(-256*x^5)/5 - (256*E^(2*E)*x^5)/125 - (96*E^(4*E)*x^5)/3125 - (16*E^(6*E)*x^5)/78125 - (E^(8*E)*x^5)/1953125
+ ((100 + E^(2*E))^4*x^5)/1953125 + (512*x^6)/3 + (512*E^(2*E)*x^6)/75 + (64*E^(4*E)*x^6)/625 + (32*E^(6*E)*x^
6)/46875 + (2*E^(8*E)*x^6)/1171875 - (2*(100 + E^(2*E))^4*x^6)/1171875 + x^2*Log[x] - 4*x^3*Log[x] - ((100 + E
^(2*E))^4*x^5*Log[x])/390625 + (4*(100 + E^(2*E))^4*x^6*Log[x])/390625

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 2341

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 2403

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{align*} \text {integral}& = \frac {\int \left (390625 x-1562500 x^2-100000000 x^4+400000000 x^5+e^{8 e} \left (-x^4+4 x^5\right )+e^{6 e} \left (-400 x^4+1600 x^5\right )+e^{4 e} \left (-60000 x^4+240000 x^5\right )+e^{2 e} \left (-4000000 x^4+16000000 x^5\right )+\left (781250 x-4687500 x^2-500000000 x^4+2400000000 x^5+e^{8 e} \left (-5 x^4+24 x^5\right )+e^{6 e} \left (-2000 x^4+9600 x^5\right )+e^{4 e} \left (-300000 x^4+1440000 x^5\right )+e^{2 e} \left (-20000000 x^4+96000000 x^5\right )\right ) \log (x)\right ) \, dx}{390625} \\ & = \frac {x^2}{2}-\frac {4 x^3}{3}-\frac {256 x^5}{5}+\frac {512 x^6}{3}+\frac {\int \left (781250 x-4687500 x^2-500000000 x^4+2400000000 x^5+e^{8 e} \left (-5 x^4+24 x^5\right )+e^{6 e} \left (-2000 x^4+9600 x^5\right )+e^{4 e} \left (-300000 x^4+1440000 x^5\right )+e^{2 e} \left (-20000000 x^4+96000000 x^5\right )\right ) \log (x) \, dx}{390625}+\frac {e^{2 e} \int \left (-4000000 x^4+16000000 x^5\right ) \, dx}{390625}+\frac {e^{4 e} \int \left (-60000 x^4+240000 x^5\right ) \, dx}{390625}+\frac {e^{6 e} \int \left (-400 x^4+1600 x^5\right ) \, dx}{390625}+\frac {e^{8 e} \int \left (-x^4+4 x^5\right ) \, dx}{390625} \\ & = \frac {x^2}{2}-\frac {4 x^3}{3}-\frac {256 x^5}{5}-\frac {256}{125} e^{2 e} x^5-\frac {96 e^{4 e} x^5}{3125}-\frac {16 e^{6 e} x^5}{78125}-\frac {e^{8 e} x^5}{1953125}+\frac {512 x^6}{3}+\frac {512}{75} e^{2 e} x^6+\frac {64}{625} e^{4 e} x^6+\frac {32 e^{6 e} x^6}{46875}+\frac {2 e^{8 e} x^6}{1171875}+\frac {\int \left (781250 x \log (x)-4687500 x^2 \log (x)-5 \left (100+e^{2 e}\right )^4 x^4 \log (x)+24 \left (100+e^{2 e}\right )^4 x^5 \log (x)\right ) \, dx}{390625} \\ & = \frac {x^2}{2}-\frac {4 x^3}{3}-\frac {256 x^5}{5}-\frac {256}{125} e^{2 e} x^5-\frac {96 e^{4 e} x^5}{3125}-\frac {16 e^{6 e} x^5}{78125}-\frac {e^{8 e} x^5}{1953125}+\frac {512 x^6}{3}+\frac {512}{75} e^{2 e} x^6+\frac {64}{625} e^{4 e} x^6+\frac {32 e^{6 e} x^6}{46875}+\frac {2 e^{8 e} x^6}{1171875}+2 \int x \log (x) \, dx-12 \int x^2 \log (x) \, dx-\frac {\left (100+e^{2 e}\right )^4 \int x^4 \log (x) \, dx}{78125}+\frac {\left (24 \left (100+e^{2 e}\right )^4\right ) \int x^5 \log (x) \, dx}{390625} \\ & = -\frac {256 x^5}{5}-\frac {256}{125} e^{2 e} x^5-\frac {96 e^{4 e} x^5}{3125}-\frac {16 e^{6 e} x^5}{78125}-\frac {e^{8 e} x^5}{1953125}+\frac {\left (100+e^{2 e}\right )^4 x^5}{1953125}+\frac {512 x^6}{3}+\frac {512}{75} e^{2 e} x^6+\frac {64}{625} e^{4 e} x^6+\frac {32 e^{6 e} x^6}{46875}+\frac {2 e^{8 e} x^6}{1171875}-\frac {2 \left (100+e^{2 e}\right )^4 x^6}{1171875}+x^2 \log (x)-4 x^3 \log (x)-\frac {\left (100+e^{2 e}\right )^4 x^5 \log (x)}{390625}+\frac {4 \left (100+e^{2 e}\right )^4 x^6 \log (x)}{390625} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.13 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.27 \[ \int \frac {390625 x-1562500 x^2-100000000 x^4+400000000 x^5+e^{8 e} \left (-x^4+4 x^5\right )+e^{6 e} \left (-400 x^4+1600 x^5\right )+e^{4 e} \left (-60000 x^4+240000 x^5\right )+e^{2 e} \left (-4000000 x^4+16000000 x^5\right )+\left (781250 x-4687500 x^2-500000000 x^4+2400000000 x^5+e^{8 e} \left (-5 x^4+24 x^5\right )+e^{6 e} \left (-2000 x^4+9600 x^5\right )+e^{4 e} \left (-300000 x^4+1440000 x^5\right )+e^{2 e} \left (-20000000 x^4+96000000 x^5\right )\right ) \log (x)}{390625} \, dx=\frac {x^2 \left (390625-1562500 x-\left (100+e^{2 e}\right )^4 x^3+4 \left (100+e^{2 e}\right )^4 x^4\right ) \log (x)}{390625} \]

[In]

Integrate[(390625*x - 1562500*x^2 - 100000000*x^4 + 400000000*x^5 + E^(8*E)*(-x^4 + 4*x^5) + E^(6*E)*(-400*x^4
+ 1600*x^5) + E^(4*E)*(-60000*x^4 + 240000*x^5) + E^(2*E)*(-4000000*x^4 + 16000000*x^5) + (781250*x - 4687500
*x^2 - 500000000*x^4 + 2400000000*x^5 + E^(8*E)*(-5*x^4 + 24*x^5) + E^(6*E)*(-2000*x^4 + 9600*x^5) + E^(4*E)*(
-300000*x^4 + 1440000*x^5) + E^(2*E)*(-20000000*x^4 + 96000000*x^5))*Log[x])/390625,x]

[Out]

(x^2*(390625 - 1562500*x - (100 + E^(2*E))^4*x^3 + 4*(100 + E^(2*E))^4*x^4)*Log[x])/390625

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(86\) vs. \(2(31)=62\).

Time = 0.58 (sec) , antiderivative size = 87, normalized size of antiderivative = 2.64

method	result	size
norman	\(x^{2} \ln \left (x \right )+\left (-\frac {{\mathrm e}^{8 \,{\mathrm e}}}{390625}-\frac {16 \,{\mathrm e}^{6 \,{\mathrm e}}}{15625}-\frac {96 \,{\mathrm e}^{4 \,{\mathrm e}}}{625}-\frac {256 \,{\mathrm e}^{2 \,{\mathrm e}}}{25}-256\right ) x^{5} \ln \left (x \right )+\left (\frac {4 \,{\mathrm e}^{8 \,{\mathrm e}}}{390625}+\frac {64 \,{\mathrm e}^{6 \,{\mathrm e}}}{15625}+\frac {384 \,{\mathrm e}^{4 \,{\mathrm e}}}{625}+\frac {1024 \,{\mathrm e}^{2 \,{\mathrm e}}}{25}+1024\right ) x^{6} \ln \left (x \right )-4 x^{3} \ln \left (x \right )\)	\(87\)
risch	\(\frac {x^{2} \left (4 \,{\mathrm e}^{8 \,{\mathrm e}} x^{4}-{\mathrm e}^{8 \,{\mathrm e}} x^{3}+1600 \,{\mathrm e}^{6 \,{\mathrm e}} x^{4}-400 \,{\mathrm e}^{6 \,{\mathrm e}} x^{3}+240000 \,{\mathrm e}^{4 \,{\mathrm e}} x^{4}-60000 \,{\mathrm e}^{4 \,{\mathrm e}} x^{3}[phone] x^{4} {\mathrm e}^{2 \,{\mathrm e}}-4000000 \,{\mathrm e}^{2 \,{\mathrm e}} x^{3}[phone] x^{4}-100000000 x^{3}-1562500 x +390625\right ) \ln \left (x \right )}{390625}\)	\(103\)
parallelrisch	\(\frac {4 \,{\mathrm e}^{8 \,{\mathrm e}} x^{6} \ln \left (x \right )}{390625}-\frac {\ln \left (x \right ) {\mathrm e}^{8 \,{\mathrm e}} x^{5}}{390625}+\frac {64 \,{\mathrm e}^{6 \,{\mathrm e}} x^{6} \ln \left (x \right )}{15625}-\frac {16 \ln \left (x \right ) {\mathrm e}^{6 \,{\mathrm e}} x^{5}}{15625}+\frac {384 \,{\mathrm e}^{4 \,{\mathrm e}} x^{6} \ln \left (x \right )}{625}-\frac {96 \ln \left (x \right ) {\mathrm e}^{4 \,{\mathrm e}} x^{5}}{625}+\frac {1024 \,{\mathrm e}^{2 \,{\mathrm e}} x^{6} \ln \left (x \right )}{25}-\frac {256 \ln \left (x \right ) {\mathrm e}^{2 \,{\mathrm e}} x^{5}}{25}+1024 x^{6} \ln \left (x \right )-256 x^{5} \ln \left (x \right )-4 x^{3} \ln \left (x \right )+x^{2} \ln \left (x \right )\)	\(125\)
default	\(\frac {24 \,{\mathrm e}^{8 \,{\mathrm e}} \left (\frac {x^{6} \ln \left (x \right )}{6}-\frac {x^{6}}{36}\right )}{390625}-\frac {{\mathrm e}^{8 \,{\mathrm e}} \left (\frac {x^{5} \ln \left (x \right )}{5}-\frac {x^{5}}{25}\right )}{78125}+\frac {384 \,{\mathrm e}^{6 \,{\mathrm e}} \left (\frac {x^{6} \ln \left (x \right )}{6}-\frac {x^{6}}{36}\right )}{15625}-\frac {16 \,{\mathrm e}^{6 \,{\mathrm e}} \left (\frac {x^{5} \ln \left (x \right )}{5}-\frac {x^{5}}{25}\right )}{3125}+\frac {2304 \,{\mathrm e}^{4 \,{\mathrm e}} \left (\frac {x^{6} \ln \left (x \right )}{6}-\frac {x^{6}}{36}\right )}{625}-\frac {96 \,{\mathrm e}^{4 \,{\mathrm e}} \left (\frac {x^{5} \ln \left (x \right )}{5}-\frac {x^{5}}{25}\right )}{125}+\frac {6144 \,{\mathrm e}^{2 \,{\mathrm e}} \left (\frac {x^{6} \ln \left (x \right )}{6}-\frac {x^{6}}{36}\right )}{25}-\frac {256 \,{\mathrm e}^{2 \,{\mathrm e}} \left (\frac {x^{5} \ln \left (x \right )}{5}-\frac {x^{5}}{25}\right )}{5}+1024 x^{6} \ln \left (x \right )-256 x^{5} \ln \left (x \right )-4 x^{3} \ln \left (x \right )+x^{2} \ln \left (x \right )+\frac {{\mathrm e}^{8 \,{\mathrm e}} \left (\frac {2}{3} x^{6}-\frac {1}{5} x^{5}\right )}{390625}+\frac {16 \,{\mathrm e}^{6 \,{\mathrm e}} \left (\frac {2}{3} x^{6}-\frac {1}{5} x^{5}\right )}{15625}+\frac {96 \,{\mathrm e}^{4 \,{\mathrm e}} \left (\frac {2}{3} x^{6}-\frac {1}{5} x^{5}\right )}{625}+\frac {256 \,{\mathrm e}^{2 \,{\mathrm e}} \left (\frac {2}{3} x^{6}-\frac {1}{5} x^{5}\right )}{25}\)	\(261\)
parts	\(\frac {24 \,{\mathrm e}^{8 \,{\mathrm e}} \left (\frac {x^{6} \ln \left (x \right )}{6}-\frac {x^{6}}{36}\right )}{390625}-\frac {{\mathrm e}^{8 \,{\mathrm e}} \left (\frac {x^{5} \ln \left (x \right )}{5}-\frac {x^{5}}{25}\right )}{78125}+\frac {384 \,{\mathrm e}^{6 \,{\mathrm e}} \left (\frac {x^{6} \ln \left (x \right )}{6}-\frac {x^{6}}{36}\right )}{15625}-\frac {16 \,{\mathrm e}^{6 \,{\mathrm e}} \left (\frac {x^{5} \ln \left (x \right )}{5}-\frac {x^{5}}{25}\right )}{3125}+\frac {2304 \,{\mathrm e}^{4 \,{\mathrm e}} \left (\frac {x^{6} \ln \left (x \right )}{6}-\frac {x^{6}}{36}\right )}{625}-\frac {96 \,{\mathrm e}^{4 \,{\mathrm e}} \left (\frac {x^{5} \ln \left (x \right )}{5}-\frac {x^{5}}{25}\right )}{125}+\frac {6144 \,{\mathrm e}^{2 \,{\mathrm e}} \left (\frac {x^{6} \ln \left (x \right )}{6}-\frac {x^{6}}{36}\right )}{25}-\frac {256 \,{\mathrm e}^{2 \,{\mathrm e}} \left (\frac {x^{5} \ln \left (x \right )}{5}-\frac {x^{5}}{25}\right )}{5}+1024 x^{6} \ln \left (x \right )-256 x^{5} \ln \left (x \right )-4 x^{3} \ln \left (x \right )+x^{2} \ln \left (x \right )-\frac {256 \,{\mathrm e}^{2 \,{\mathrm e}} x^{5}}{125}+\frac {512 \,{\mathrm e}^{2 \,{\mathrm e}} x^{6}}{75}-\frac {96 \,{\mathrm e}^{4 \,{\mathrm e}} x^{5}}{3125}+\frac {64 \,{\mathrm e}^{4 \,{\mathrm e}} x^{6}}{625}-\frac {16 \,{\mathrm e}^{6 \,{\mathrm e}} x^{5}}{78125}+\frac {32 \,{\mathrm e}^{6 \,{\mathrm e}} x^{6}}{46875}-\frac {{\mathrm e}^{8 \,{\mathrm e}} x^{5}}{1953125}+\frac {2 \,{\mathrm e}^{8 \,{\mathrm e}} x^{6}}{1171875}\)	\(269\)

[In]

int(1/390625*((24*x^5-5*x^4)*exp(exp(1))^8+(9600*x^5-2000*x^4)*exp(exp(1))^6+(1440000*x^5-300000*x^4)*exp(exp(
1))^4+(96000000*x^5-20000000*x^4)*exp(exp(1))^2+2400000000*x^5-500000000*x^4-4687500*x^2+781250*x)*ln(x)+1/390
625*(4*x^5-x^4)*exp(exp(1))^8+1/390625*(1600*x^5-400*x^4)*exp(exp(1))^6+1/390625*(240000*x^5-60000*x^4)*exp(ex
p(1))^4+1/390625*(16000000*x^5-4000000*x^4)*exp(exp(1))^2+1024*x^5-256*x^4-4*x^2+x,x,method=_RETURNVERBOSE)

[Out]

x^2*ln(x)+(-1/390625*exp(exp(1))^8-16/15625*exp(exp(1))^6-96/625*exp(exp(1))^4-256/25*exp(exp(1))^2-256)*x^5*l
n(x)+(4/390625*exp(exp(1))^8+64/15625*exp(exp(1))^6+384/625*exp(exp(1))^4+1024/25*exp(exp(1))^2+1024)*x^6*ln(x
)-4*x^3*ln(x)

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 96 vs. \(2 (30) = 60\).

Time = 0.26 (sec) , antiderivative size = 96, normalized size of antiderivative = 2.91 \[ \int \frac {390625 x-1562500 x^2-100000000 x^4+400000000 x^5+e^{8 e} \left (-x^4+4 x^5\right )+e^{6 e} \left (-400 x^4+1600 x^5\right )+e^{4 e} \left (-60000 x^4+240000 x^5\right )+e^{2 e} \left (-4000000 x^4+16000000 x^5\right )+\left (781250 x-4687500 x^2-500000000 x^4+2400000000 x^5+e^{8 e} \left (-5 x^4+24 x^5\right )+e^{6 e} \left (-2000 x^4+9600 x^5\right )+e^{4 e} \left (-300000 x^4+1440000 x^5\right )+e^{2 e} \left (-20000000 x^4+96000000 x^5\right )\right ) \log (x)}{390625} \, dx=\frac {1}{390625} \, {\left (400000000 \, x^{6} - 100000000 \, x^{5} - 1562500 \, x^{3} + 390625 \, x^{2} + {\left (4 \, x^{6} - x^{5}\right )} e^{\left (8 \, e\right )} + 400 \, {\left (4 \, x^{6} - x^{5}\right )} e^{\left (6 \, e\right )} + 60000 \, {\left (4 \, x^{6} - x^{5}\right )} e^{\left (4 \, e\right )} + 4000000 \, {\left (4 \, x^{6} - x^{5}\right )} e^{\left (2 \, e\right )}\right )} \log \left (x\right ) \]

[In]

integrate(1/390625*((24*x^5-5*x^4)*exp(exp(1))^8+(9600*x^5-2000*x^4)*exp(exp(1))^6+(1440000*x^5-300000*x^4)*ex
p(exp(1))^4+(96000000*x^5-20000000*x^4)*exp(exp(1))^2+2400000000*x^5-500000000*x^4-4687500*x^2+781250*x)*log(x
)+1/390625*(4*x^5-x^4)*exp(exp(1))^8+1/390625*(1600*x^5-400*x^4)*exp(exp(1))^6+1/390625*(240000*x^5-60000*x^4)
*exp(exp(1))^4+1/390625*(16000000*x^5-4000000*x^4)*exp(exp(1))^2+1024*x^5-256*x^4-4*x^2+x,x, algorithm="fricas
")

[Out]

1/390625*(400000000*x^6 - 100000000*x^5 - 1562500*x^3 + 390625*x^2 + (4*x^6 - x^5)*e^(8*e) + 400*(4*x^6 - x^5)
*e^(6*e) + 60000*(4*x^6 - x^5)*e^(4*e) + 4000000*(4*x^6 - x^5)*e^(2*e))*log(x)

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 128 vs. \(2 (26) = 52\).

Time = 0.20 (sec) , antiderivative size = 128, normalized size of antiderivative = 3.88 \[ \int \frac {390625 x-1562500 x^2-100000000 x^4+400000000 x^5+e^{8 e} \left (-x^4+4 x^5\right )+e^{6 e} \left (-400 x^4+1600 x^5\right )+e^{4 e} \left (-60000 x^4+240000 x^5\right )+e^{2 e} \left (-4000000 x^4+16000000 x^5\right )+\left (781250 x-4687500 x^2-500000000 x^4+2400000000 x^5+e^{8 e} \left (-5 x^4+24 x^5\right )+e^{6 e} \left (-2000 x^4+9600 x^5\right )+e^{4 e} \left (-300000 x^4+1440000 x^5\right )+e^{2 e} \left (-20000000 x^4+96000000 x^5\right )\right ) \log (x)}{390625} \, dx=\left (1024 x^{6} + \frac {1024 x^{6} e^{2 e}}{25} + \frac {4 x^{6} e^{8 e}}{390625} + \frac {384 x^{6} e^{4 e}}{625} + \frac {64 x^{6} e^{6 e}}{15625} - \frac {16 x^{5} e^{6 e}}{15625} - \frac {96 x^{5} e^{4 e}}{625} - \frac {x^{5} e^{8 e}}{390625} - \frac {256 x^{5} e^{2 e}}{25} - 256 x^{5} - 4 x^{3} + x^{2}\right ) \log {\left (x \right )} \]

[In]

integrate(1/390625*((24*x**5-5*x**4)*exp(exp(1))**8+(9600*x**5-2000*x**4)*exp(exp(1))**6+(1440000*x**5-300000*
x**4)*exp(exp(1))**4+(96000000*x**5-20000000*x**4)*exp(exp(1))**2+2400000000*x**5-500000000*x**4-4687500*x**2+
781250*x)*ln(x)+1/390625*(4*x**5-x**4)*exp(exp(1))**8+1/390625*(1600*x**5-400*x**4)*exp(exp(1))**6+1/390625*(2
40000*x**5-60000*x**4)*exp(exp(1))**4+1/390625*(16000000*x**5-4000000*x**4)*exp(exp(1))**2+1024*x**5-256*x**4-
4*x**2+x,x)

[Out]

(1024*x**6 + 1024*x**6*exp(2*E)/25 + 4*x**6*exp(8*E)/390625 + 384*x**6*exp(4*E)/625 + 64*x**6*exp(6*E)/15625 -
16*x**5*exp(6*E)/15625 - 96*x**5*exp(4*E)/625 - x**5*exp(8*E)/390625 - 256*x**5*exp(2*E)/25 - 256*x**5 - 4*x*
*3 + x**2)*log(x)

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 245 vs. \(2 (30) = 60\).

Time = 0.18 (sec) , antiderivative size = 245, normalized size of antiderivative = 7.42 \[ \int \frac {390625 x-1562500 x^2-100000000 x^4+400000000 x^5+e^{8 e} \left (-x^4+4 x^5\right )+e^{6 e} \left (-400 x^4+1600 x^5\right )+e^{4 e} \left (-60000 x^4+240000 x^5\right )+e^{2 e} \left (-4000000 x^4+16000000 x^5\right )+\left (781250 x-4687500 x^2-500000000 x^4+2400000000 x^5+e^{8 e} \left (-5 x^4+24 x^5\right )+e^{6 e} \left (-2000 x^4+9600 x^5\right )+e^{4 e} \left (-300000 x^4+1440000 x^5\right )+e^{2 e} \left (-20000000 x^4+96000000 x^5\right )\right ) \log (x)}{390625} \, dx=-\frac {2}{1171875} \, x^{6} {\left (e^{\left (8 \, e\right )} + 400 \, e^{\left (6 \, e\right )} + 60000 \, e^{\left (4 \, e\right )} + 4000000 \, e^{\left (2 \, e\right )} + 100000000\right )} + \frac {512}{3} \, x^{6} + \frac {1}{1953125} \, x^{5} {\left (e^{\left (8 \, e\right )} + 400 \, e^{\left (6 \, e\right )} + 60000 \, e^{\left (4 \, e\right )} + 4000000 \, e^{\left (2 \, e\right )} + 100000000\right )} - \frac {256}{5} \, x^{5} + \frac {1}{5859375} \, {\left (10 \, x^{6} - 3 \, x^{5}\right )} e^{\left (8 \, e\right )} + \frac {16}{234375} \, {\left (10 \, x^{6} - 3 \, x^{5}\right )} e^{\left (6 \, e\right )} + \frac {32}{3125} \, {\left (10 \, x^{6} - 3 \, x^{5}\right )} e^{\left (4 \, e\right )} + \frac {256}{375} \, {\left (10 \, x^{6} - 3 \, x^{5}\right )} e^{\left (2 \, e\right )} + \frac {1}{390625} \, {\left (400000000 \, x^{6} - 100000000 \, x^{5} - 1562500 \, x^{3} + 390625 \, x^{2} + {\left (4 \, x^{6} - x^{5}\right )} e^{\left (8 \, e\right )} + 400 \, {\left (4 \, x^{6} - x^{5}\right )} e^{\left (6 \, e\right )} + 60000 \, {\left (4 \, x^{6} - x^{5}\right )} e^{\left (4 \, e\right )} + 4000000 \, {\left (4 \, x^{6} - x^{5}\right )} e^{\left (2 \, e\right )}\right )} \log \left (x\right ) \]

[In]

integrate(1/390625*((24*x^5-5*x^4)*exp(exp(1))^8+(9600*x^5-2000*x^4)*exp(exp(1))^6+(1440000*x^5-300000*x^4)*ex
p(exp(1))^4+(96000000*x^5-20000000*x^4)*exp(exp(1))^2+2400000000*x^5-500000000*x^4-4687500*x^2+781250*x)*log(x
)+1/390625*(4*x^5-x^4)*exp(exp(1))^8+1/390625*(1600*x^5-400*x^4)*exp(exp(1))^6+1/390625*(240000*x^5-60000*x^4)
*exp(exp(1))^4+1/390625*(16000000*x^5-4000000*x^4)*exp(exp(1))^2+1024*x^5-256*x^4-4*x^2+x,x, algorithm="maxima
")

[Out]

-2/1171875*x^6*(e^(8*e) + 400*e^(6*e) + 60000*e^(4*e) + 4000000*e^(2*e) + 100000000) + 512/3*x^6 + 1/1953125*x
^5*(e^(8*e) + 400*e^(6*e) + 60000*e^(4*e) + 4000000*e^(2*e) + 100000000) - 256/5*x^5 + 1/5859375*(10*x^6 - 3*x
^5)*e^(8*e) + 16/234375*(10*x^6 - 3*x^5)*e^(6*e) + 32/3125*(10*x^6 - 3*x^5)*e^(4*e) + 256/375*(10*x^6 - 3*x^5)
*e^(2*e) + 1/390625*(400000000*x^6 - 100000000*x^5 - 1562500*x^3 + 390625*x^2 + (4*x^6 - x^5)*e^(8*e) + 400*(4
*x^6 - x^5)*e^(6*e) + 60000*(4*x^6 - x^5)*e^(4*e) + 4000000*(4*x^6 - x^5)*e^(2*e))*log(x)

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 276 vs. \(2 (30) = 60\).

Time = 0.26 (sec) , antiderivative size = 276, normalized size of antiderivative = 8.36 \[ \int \frac {390625 x-1562500 x^2-100000000 x^4+400000000 x^5+e^{8 e} \left (-x^4+4 x^5\right )+e^{6 e} \left (-400 x^4+1600 x^5\right )+e^{4 e} \left (-60000 x^4+240000 x^5\right )+e^{2 e} \left (-4000000 x^4+16000000 x^5\right )+\left (781250 x-4687500 x^2-500000000 x^4+2400000000 x^5+e^{8 e} \left (-5 x^4+24 x^5\right )+e^{6 e} \left (-2000 x^4+9600 x^5\right )+e^{4 e} \left (-300000 x^4+1440000 x^5\right )+e^{2 e} \left (-20000000 x^4+96000000 x^5\right )\right ) \log (x)}{390625} \, dx=\frac {4}{390625} \, x^{6} e^{\left (8 \, e\right )} \log \left (x\right ) + \frac {64}{15625} \, x^{6} e^{\left (6 \, e\right )} \log \left (x\right ) + \frac {384}{625} \, x^{6} e^{\left (4 \, e\right )} \log \left (x\right ) + \frac {1024}{25} \, x^{6} e^{\left (2 \, e\right )} \log \left (x\right ) - \frac {2}{1171875} \, x^{6} e^{\left (8 \, e\right )} - \frac {32}{46875} \, x^{6} e^{\left (6 \, e\right )} - \frac {64}{625} \, x^{6} e^{\left (4 \, e\right )} - \frac {512}{75} \, x^{6} e^{\left (2 \, e\right )} + 1024 \, x^{6} \log \left (x\right ) - \frac {1}{390625} \, x^{5} e^{\left (8 \, e\right )} \log \left (x\right ) - \frac {16}{15625} \, x^{5} e^{\left (6 \, e\right )} \log \left (x\right ) - \frac {96}{625} \, x^{5} e^{\left (4 \, e\right )} \log \left (x\right ) - \frac {256}{25} \, x^{5} e^{\left (2 \, e\right )} \log \left (x\right ) + \frac {1}{1953125} \, x^{5} e^{\left (8 \, e\right )} + \frac {16}{78125} \, x^{5} e^{\left (6 \, e\right )} + \frac {96}{3125} \, x^{5} e^{\left (4 \, e\right )} + \frac {256}{125} \, x^{5} e^{\left (2 \, e\right )} - 256 \, x^{5} \log \left (x\right ) - 4 \, x^{3} \log \left (x\right ) + x^{2} \log \left (x\right ) + \frac {1}{5859375} \, {\left (10 \, x^{6} - 3 \, x^{5}\right )} e^{\left (8 \, e\right )} + \frac {16}{234375} \, {\left (10 \, x^{6} - 3 \, x^{5}\right )} e^{\left (6 \, e\right )} + \frac {32}{3125} \, {\left (10 \, x^{6} - 3 \, x^{5}\right )} e^{\left (4 \, e\right )} + \frac {256}{375} \, {\left (10 \, x^{6} - 3 \, x^{5}\right )} e^{\left (2 \, e\right )} \]

[In]

integrate(1/390625*((24*x^5-5*x^4)*exp(exp(1))^8+(9600*x^5-2000*x^4)*exp(exp(1))^6+(1440000*x^5-300000*x^4)*ex
p(exp(1))^4+(96000000*x^5-20000000*x^4)*exp(exp(1))^2+2400000000*x^5-500000000*x^4-4687500*x^2+781250*x)*log(x
)+1/390625*(4*x^5-x^4)*exp(exp(1))^8+1/390625*(1600*x^5-400*x^4)*exp(exp(1))^6+1/390625*(240000*x^5-60000*x^4)
*exp(exp(1))^4+1/390625*(16000000*x^5-4000000*x^4)*exp(exp(1))^2+1024*x^5-256*x^4-4*x^2+x,x, algorithm="giac")

[Out]

4/390625*x^6*e^(8*e)*log(x) + 64/15625*x^6*e^(6*e)*log(x) + 384/625*x^6*e^(4*e)*log(x) + 1024/25*x^6*e^(2*e)*l
og(x) - 2/1171875*x^6*e^(8*e) - 32/46875*x^6*e^(6*e) - 64/625*x^6*e^(4*e) - 512/75*x^6*e^(2*e) + 1024*x^6*log(
x) - 1/390625*x^5*e^(8*e)*log(x) - 16/15625*x^5*e^(6*e)*log(x) - 96/625*x^5*e^(4*e)*log(x) - 256/25*x^5*e^(2*e
)*log(x) + 1/1953125*x^5*e^(8*e) + 16/78125*x^5*e^(6*e) + 96/3125*x^5*e^(4*e) + 256/125*x^5*e^(2*e) - 256*x^5*
log(x) - 4*x^3*log(x) + x^2*log(x) + 1/5859375*(10*x^6 - 3*x^5)*e^(8*e) + 16/234375*(10*x^6 - 3*x^5)*e^(6*e) +
32/3125*(10*x^6 - 3*x^5)*e^(4*e) + 256/375*(10*x^6 - 3*x^5)*e^(2*e)

Mupad [B] (verification not implemented)

Time = 9.25 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.39 \[ \int \frac {390625 x-1562500 x^2-100000000 x^4+400000000 x^5+e^{8 e} \left (-x^4+4 x^5\right )+e^{6 e} \left (-400 x^4+1600 x^5\right )+e^{4 e} \left (-60000 x^4+240000 x^5\right )+e^{2 e} \left (-4000000 x^4+16000000 x^5\right )+\left (781250 x-4687500 x^2-500000000 x^4+2400000000 x^5+e^{8 e} \left (-5 x^4+24 x^5\right )+e^{6 e} \left (-2000 x^4+9600 x^5\right )+e^{4 e} \left (-300000 x^4+1440000 x^5\right )+e^{2 e} \left (-20000000 x^4+96000000 x^5\right )\right ) \log (x)}{390625} \, dx=x^2\,\ln \left (x\right )-4\,x^3\,\ln \left (x\right )-\frac {x^5\,\ln \left (x\right )\,{\left ({\mathrm {e}}^{2\,\mathrm {e}}+100\right )}^4}{390625}+\frac {4\,x^6\,\ln \left (x\right )\,{\left ({\mathrm {e}}^{2\,\mathrm {e}}+100\right )}^4}{390625} \]

[In]

int(x - (log(x)*(exp(8*exp(1))*(5*x^4 - 24*x^5) - 781250*x + exp(6*exp(1))*(2000*x^4 - 9600*x^5) + exp(4*exp(1
))*(300000*x^4 - 1440000*x^5) + exp(2*exp(1))*(20000000*x^4 - 96000000*x^5) + 4687500*x^2 + 500000000*x^4 - 24
00000000*x^5))/390625 - (exp(6*exp(1))*(400*x^4 - 1600*x^5))/390625 - (exp(4*exp(1))*(60000*x^4 - 240000*x^5))
/390625 - (exp(2*exp(1))*(4000000*x^4 - 16000000*x^5))/390625 - 4*x^2 - 256*x^4 + 1024*x^5 - (exp(8*exp(1))*(x
^4 - 4*x^5))/390625,x)

[Out]

x^2*log(x) - 4*x^3*log(x) - (x^5*log(x)*(exp(2*exp(1)) + 100)^4)/390625 + (4*x^6*log(x)*(exp(2*exp(1)) + 100)^
4)/390625