∫ ( x2__ e3+x) 1 ___36 (900+132x+x2)(900x+132x2+x3+e3(1800+264x+2x2)+(132x2+2x3+e3(132x+2x2)) log( x2__ e3+x)) _________________________________________________________________________________________________________________________________________

Optimal. Leaf size=25 \[ \left (\frac {x^2}{e^3+x}\right )^{\left (5+\frac {x}{6}\right )^2+2 x} \]

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Rubi [F] time = 180.00, 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*} \text {\$Aborted} \end {gather*}

Int[((x^2/(E^3 + x))^((900 + 132*x + x^2)/36)*(900*x + 132*x^2 + x^3 + E^3*(1800 + 264*x + 2*x^2) + (132*x^2 +

2*x^3 + E^3*(132*x + 2*x^2))*Log[x^2/(E^3 + x)]))/(36*E^3*x + 36*x^2),x]

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Mathematica [A] time = 5.15, size = 31, normalized size = 1.24 \begin {gather*} \frac {x^{50} \left (\frac {x^2}{e^3+x}\right )^{\frac {1}{36} x (132+x)}}{\left (e^3+x\right )^{25}} \end {gather*}

Integrate[((x^2/(E^3 + x))^((900 + 132*x + x^2)/36)*(900*x + 132*x^2 + x^3 + E^3*(1800 + 264*x + 2*x^2) + (132

*x^2 + 2*x^3 + E^3*(132*x + 2*x^2))*Log[x^2/(E^3 + x)]))/(36*E^3*x + 36*x^2),x]

(x^50*(x^2/(E^3 + x))^((x*(132 + x))/36))/(E^3 + x)^25

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fricas [A] time = 0.63, size = 21, normalized size = 0.84 \begin {gather*} \left (\frac {x^{2}}{x + e^{3}}\right )^{\frac {1}{36} \, x^{2} + \frac {11}{3} \, x + 25} \end {gather*}

integrate((((2*x^2+132*x)*exp(3)+2*x^3+132*x^2)*log(x^2/(exp(3)+x))+(2*x^2+264*x+1800)*exp(3)+x^3+132*x^2+900*

x)*exp(1/36*(x^2+132*x+900)*log(x^2/(exp(3)+x)))/(36*x*exp(3)+36*x^2),x, algorithm="fricas")

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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {{\left (x^{3} + 132 \, x^{2} + 2 \, {\left (x^{2} + 132 \, x + 900\right )} e^{3} + 2 \, {\left (x^{3} + 66 \, x^{2} + {\left (x^{2} + 66 \, x\right )} e^{3}\right )} \log \left (\frac {x^{2}}{x + e^{3}}\right ) + 900 \, x\right )} \left (\frac {x^{2}}{x + e^{3}}\right )^{\frac {1}{36} \, x^{2} + \frac {11}{3} \, x + 25}}{36 \, {\left (x^{2} + x e^{3}\right )}}\,{d x} \end {gather*}

integrate((((2*x^2+132*x)*exp(3)+2*x^3+132*x^2)*log(x^2/(exp(3)+x))+(2*x^2+264*x+1800)*exp(3)+x^3+132*x^2+900*

x)*exp(1/36*(x^2+132*x+900)*log(x^2/(exp(3)+x)))/(36*x*exp(3)+36*x^2),x, algorithm="giac")

integrate(1/36*(x^3 + 132*x^2 + 2*(x^2 + 132*x + 900)*e^3 + 2*(x^3 + 66*x^2 + (x^2 + 66*x)*e^3)*log(x^2/(x + e

^3)) + 900*x)*(x^2/(x + e^3))^(1/36*x^2 + 11/3*x + 25)/(x^2 + x*e^3), x)

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method	result	size

risch	$\left (\frac {x^{2}}{{\mathrm e}^{3}+x}\right )^{\frac {1}{36} x^{2}+\frac {11}{3} x +25}$	$22$
norman	${\mathrm e}^{\frac {\left (x^{2}+132 x +900\right ) \ln \left (\frac {x^{2}}{{\mathrm e}^{3}+x}\right )}{36}}$	$23$

int((((2*x^2+132*x)*exp(3)+2*x^3+132*x^2)*ln(x^2/(exp(3)+x))+(2*x^2+264*x+1800)*exp(3)+x^3+132*x^2+900*x)*exp(

1/36*(x^2+132*x+900)*ln(x^2/(exp(3)+x)))/(36*x*exp(3)+36*x^2),x,method=_RETURNVERBOSE)

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maxima [B] time = 0.65, size = 210, normalized size = 8.40 \begin {gather*} \frac {x^{50} e^{\left (-\frac {1}{36} \, x^{2} \log \left (x + e^{3}\right ) + \frac {1}{18} \, x^{2} \log \relax (x) - \frac {11}{3} \, x \log \left (x + e^{3}\right ) + \frac {22}{3} \, x \log \relax (x)\right )}}{x^{25} + 25 \, x^{24} e^{3} + 300 \, x^{23} e^{6} + 2300 \, x^{22} e^{9} + 12650 \, x^{21} e^{12} + 53130 \, x^{20} e^{15} + 177100 \, x^{19} e^{18} + 480700 \, x^{18} e^{21} + 1081575 \, x^{17} e^{24} + 2042975 \, x^{16} e^{27} + 3268760 \, x^{15} e^{30} + 4457400 \, x^{14} e^{33} + 5200300 \, x^{13} e^{36} + 5200300 \, x^{12} e^{39} + 4457400 \, x^{11} e^{42} + 3268760 \, x^{10} e^{45} + 2042975 \, x^{9} e^{48} + 1081575 \, x^{8} e^{51} + 480700 \, x^{7} e^{54} + 177100 \, x^{6} e^{57} + 53130 \, x^{5} e^{60} + 12650 \, x^{4} e^{63} + 2300 \, x^{3} e^{66} + 300 \, x^{2} e^{69} + 25 \, x e^{72} + e^{75}} \end {gather*}

integrate((((2*x^2+132*x)*exp(3)+2*x^3+132*x^2)*log(x^2/(exp(3)+x))+(2*x^2+264*x+1800)*exp(3)+x^3+132*x^2+900*

x)*exp(1/36*(x^2+132*x+900)*log(x^2/(exp(3)+x)))/(36*x*exp(3)+36*x^2),x, algorithm="maxima")

x^50*e^(-1/36*x^2*log(x + e^3) + 1/18*x^2*log(x) - 11/3*x*log(x + e^3) + 22/3*x*log(x))/(x^25 + 25*x^24*e^3 +

300*x^23*e^6 + 2300*x^22*e^9 + 12650*x^21*e^12 + 53130*x^20*e^15 + 177100*x^19*e^18 + 480700*x^18*e^21 + 10815

75*x^17*e^24 + 2042975*x^16*e^27 + 3268760*x^15*e^30 + 4457400*x^14*e^33 + 5200300*x^13*e^36 + 5200300*x^12*e^

39 + 4457400*x^11*e^42 + 3268760*x^10*e^45 + 2042975*x^9*e^48 + 1081575*x^8*e^51 + 480700*x^7*e^54 + 177100*x^

6*e^57 + 53130*x^5*e^60 + 12650*x^4*e^63 + 2300*x^3*e^66 + 300*x^2*e^69 + 25*x*e^72 + e^75)

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mupad [B] time = 5.06, size = 217, normalized size = 8.68 \begin {gather*} \frac {x^{50}\,{\mathrm {e}}^{\frac {11\,x\,\ln \left (\frac {1}{x+{\mathrm {e}}^3}\right )}{3}}\,{\left (\frac {1}{x+{\mathrm {e}}^3}\right )}^{\frac {x^2}{36}}\,{\left (x^2\right )}^{\frac {11\,x}{3}}\,{\left (x^2\right )}^{\frac {x^2}{36}}}{x^{25}+25\,{\mathrm {e}}^3\,x^{24}+300\,{\mathrm {e}}^6\,x^{23}+2300\,{\mathrm {e}}^9\,x^{22}+12650\,{\mathrm {e}}^{12}\,x^{21}+53130\,{\mathrm {e}}^{15}\,x^{20}+177100\,{\mathrm {e}}^{18}\,x^{19}+480700\,{\mathrm {e}}^{21}\,x^{18}+1081575\,{\mathrm {e}}^{24}\,x^{17}+2042975\,{\mathrm {e}}^{27}\,x^{16}+3268760\,{\mathrm {e}}^{30}\,x^{15}+4457400\,{\mathrm {e}}^{33}\,x^{14}+5200300\,{\mathrm {e}}^{36}\,x^{13}+5200300\,{\mathrm {e}}^{39}\,x^{12}+4457400\,{\mathrm {e}}^{42}\,x^{11}+3268760\,{\mathrm {e}}^{45}\,x^{10}+2042975\,{\mathrm {e}}^{48}\,x^9+1081575\,{\mathrm {e}}^{51}\,x^8+480700\,{\mathrm {e}}^{54}\,x^7+177100\,{\mathrm {e}}^{57}\,x^6+53130\,{\mathrm {e}}^{60}\,x^5+12650\,{\mathrm {e}}^{63}\,x^4+2300\,{\mathrm {e}}^{66}\,x^3+300\,{\mathrm {e}}^{69}\,x^2+25\,{\mathrm {e}}^{72}\,x+{\mathrm {e}}^{75}} \end {gather*}

int((exp((log(x^2/(x + exp(3)))*(132*x + x^2 + 900))/36)*(900*x + exp(3)*(264*x + 2*x^2 + 1800) + log(x^2/(x +

exp(3)))*(exp(3)*(132*x + 2*x^2) + 132*x^2 + 2*x^3) + 132*x^2 + x^3))/(36*x*exp(3) + 36*x^2),x)

(x^50*exp((11*x*log(1/(x + exp(3))))/3)*(1/(x + exp(3)))^(x^2/36)*(x^2)^((11*x)/3)*(x^2)^(x^2/36))/(exp(75) +

25*x*exp(72) + 25*x^24*exp(3) + 300*x^23*exp(6) + 2300*x^22*exp(9) + 12650*x^21*exp(12) + 53130*x^20*exp(15) +

177100*x^19*exp(18) + 480700*x^18*exp(21) + 1081575*x^17*exp(24) + 2042975*x^16*exp(27) + 3268760*x^15*exp(30

) + 4457400*x^14*exp(33) + 5200300*x^13*exp(36) + 5200300*x^12*exp(39) + 4457400*x^11*exp(42) + 3268760*x^10*e

xp(45) + 2042975*x^9*exp(48) + 1081575*x^8*exp(51) + 480700*x^7*exp(54) + 177100*x^6*exp(57) + 53130*x^5*exp(6

0) + 12650*x^4*exp(63) + 2300*x^3*exp(66) + 300*x^2*exp(69) + x^25)

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sympy [A] time = 0.86, size = 22, normalized size = 0.88 \begin {gather*} e^{\left (\frac {x^{2}}{36} + \frac {11 x}{3} + 25\right ) \log {\left (\frac {x^{2}}{x + e^{3}} \right )}} \end {gather*}

integrate((((2*x**2+132*x)*exp(3)+2*x**3+132*x**2)*ln(x**2/(exp(3)+x))+(2*x**2+264*x+1800)*exp(3)+x**3+132*x**

2+900*x)*exp(1/36*(x**2+132*x+900)*ln(x**2/(exp(3)+x)))/(36*x*exp(3)+36*x**2),x)

exp((x**2/36 + 11*x/3 + 25)*log(x**2/(x + exp(3))))

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3.71.22 \(\int \frac {(\frac {x^2}{e^3+x})^{\frac {1}{36} (900+132 x+x^2)} (900 x+132 x^2+x^3+e^3 (1800+264 x+2 x^2)+(132 x^2+2 x^3+e^3 (132 x+2 x^2)) \log (\frac {x^2}{e^3+x}))}{36 e^3 x+36 x^2} \, dx\)