Optimal. Leaf size=29 \[ 3+e^{4 \left (\log (4)+\left (2-x+(5+x)^2\right ) \log \left (25 e^{-x} x\right )\right )} \]
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Rubi [F] time = 4.03, 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 {256\ 25^{108+36 x+4 x^2} \left (e^{-x} x\right )^{108+36 x+4 x^2} \left (108-72 x-32 x^2-4 x^3+\left (36 x+8 x^2\right ) \log \left (25 e^{-x} x\right )\right )}{x} \, dx \end {gather*}
Verification is not applicable to the result.
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\begin {gather*} \begin {aligned} \text {integral} &=256 \int \frac {25^{108+36 x+4 x^2} \left (e^{-x} x\right )^{108+36 x+4 x^2} \left (108-72 x-32 x^2-4 x^3+\left (36 x+8 x^2\right ) \log \left (25 e^{-x} x\right )\right )}{x} \, dx\\ &=256 \int \left (-\frac {4\ 25^{108+36 x+4 x^2} \left (e^{-x} x\right )^{108+36 x+4 x^2} \left (-27+18 x+8 x^2+x^3\right )}{x}+4\ 25^{108+36 x+4 x^2} \left (e^{-x} x\right )^{108+36 x+4 x^2} (9+2 x) \log \left (25 e^{-x} x\right )\right ) \, dx\\ &=-\left (1024 \int \frac {25^{108+36 x+4 x^2} \left (e^{-x} x\right )^{108+36 x+4 x^2} \left (-27+18 x+8 x^2+x^3\right )}{x} \, dx\right )+1024 \int 25^{108+36 x+4 x^2} \left (e^{-x} x\right )^{108+36 x+4 x^2} (9+2 x) \log \left (25 e^{-x} x\right ) \, dx\\ &=-\left (1024 \int \left (18\ 25^{108+36 x+4 x^2} \left (e^{-x} x\right )^{108+36 x+4 x^2}-\frac {27\ 25^{108+36 x+4 x^2} \left (e^{-x} x\right )^{108+36 x+4 x^2}}{x}+8\ 25^{108+36 x+4 x^2} x \left (e^{-x} x\right )^{108+36 x+4 x^2}+25^{108+36 x+4 x^2} x^2 \left (e^{-x} x\right )^{108+36 x+4 x^2}\right ) \, dx\right )-1024 \int \frac {(1-x) \left (9 \int 25^{4 \left (27+9 x+x^2\right )} \left (e^{-x} x\right )^{4 \left (27+9 x+x^2\right )} \, dx+2 \int 25^{4 \left (27+9 x+x^2\right )} x \left (e^{-x} x\right )^{4 \left (27+9 x+x^2\right )} \, dx\right )}{x} \, dx+\left (2048 \log \left (25 e^{-x} x\right )\right ) \int 25^{108+36 x+4 x^2} x \left (e^{-x} x\right )^{108+36 x+4 x^2} \, dx+\left (9216 \log \left (25 e^{-x} x\right )\right ) \int 25^{108+36 x+4 x^2} \left (e^{-x} x\right )^{108+36 x+4 x^2} \, dx\\ &=-\left (1024 \int 25^{108+36 x+4 x^2} x^2 \left (e^{-x} x\right )^{108+36 x+4 x^2} \, dx\right )-1024 \int \left (-\frac {9 (-1+x) \int 25^{4 \left (27+9 x+x^2\right )} \left (e^{-x} x\right )^{4 \left (27+9 x+x^2\right )} \, dx}{x}-\frac {2 (-1+x) \int 25^{4 \left (27+9 x+x^2\right )} x \left (e^{-x} x\right )^{4 \left (27+9 x+x^2\right )} \, dx}{x}\right ) \, dx-8192 \int 25^{108+36 x+4 x^2} x \left (e^{-x} x\right )^{108+36 x+4 x^2} \, dx-18432 \int 25^{108+36 x+4 x^2} \left (e^{-x} x\right )^{108+36 x+4 x^2} \, dx+27648 \int \frac {25^{108+36 x+4 x^2} \left (e^{-x} x\right )^{108+36 x+4 x^2}}{x} \, dx+\left (2048 \log \left (25 e^{-x} x\right )\right ) \int 25^{108+36 x+4 x^2} x \left (e^{-x} x\right )^{108+36 x+4 x^2} \, dx+\left (9216 \log \left (25 e^{-x} x\right )\right ) \int 25^{108+36 x+4 x^2} \left (e^{-x} x\right )^{108+36 x+4 x^2} \, dx\\ &=-\left (1024 \int 25^{108+36 x+4 x^2} x^2 \left (e^{-x} x\right )^{108+36 x+4 x^2} \, dx\right )+2048 \int \frac {(-1+x) \int 25^{4 \left (27+9 x+x^2\right )} x \left (e^{-x} x\right )^{4 \left (27+9 x+x^2\right )} \, dx}{x} \, dx-8192 \int 25^{108+36 x+4 x^2} x \left (e^{-x} x\right )^{108+36 x+4 x^2} \, dx+9216 \int \frac {(-1+x) \int 25^{4 \left (27+9 x+x^2\right )} \left (e^{-x} x\right )^{4 \left (27+9 x+x^2\right )} \, dx}{x} \, dx-18432 \int 25^{108+36 x+4 x^2} \left (e^{-x} x\right )^{108+36 x+4 x^2} \, dx+27648 \int \frac {25^{108+36 x+4 x^2} \left (e^{-x} x\right )^{108+36 x+4 x^2}}{x} \, dx+\left (2048 \log \left (25 e^{-x} x\right )\right ) \int 25^{108+36 x+4 x^2} x \left (e^{-x} x\right )^{108+36 x+4 x^2} \, dx+\left (9216 \log \left (25 e^{-x} x\right )\right ) \int 25^{108+36 x+4 x^2} \left (e^{-x} x\right )^{108+36 x+4 x^2} \, dx\\ &=-\left (1024 \int 25^{108+36 x+4 x^2} x^2 \left (e^{-x} x\right )^{108+36 x+4 x^2} \, dx\right )+2048 \int \left (\int 25^{4 \left (27+9 x+x^2\right )} x \left (e^{-x} x\right )^{4 \left (27+9 x+x^2\right )} \, dx-\frac {\int 25^{4 \left (27+9 x+x^2\right )} x \left (e^{-x} x\right )^{4 \left (27+9 x+x^2\right )} \, dx}{x}\right ) \, dx-8192 \int 25^{108+36 x+4 x^2} x \left (e^{-x} x\right )^{108+36 x+4 x^2} \, dx+9216 \int \left (\int 25^{4 \left (27+9 x+x^2\right )} \left (e^{-x} x\right )^{4 \left (27+9 x+x^2\right )} \, dx-\frac {\int 25^{4 \left (27+9 x+x^2\right )} \left (e^{-x} x\right )^{4 \left (27+9 x+x^2\right )} \, dx}{x}\right ) \, dx-18432 \int 25^{108+36 x+4 x^2} \left (e^{-x} x\right )^{108+36 x+4 x^2} \, dx+27648 \int \frac {25^{108+36 x+4 x^2} \left (e^{-x} x\right )^{108+36 x+4 x^2}}{x} \, dx+\left (2048 \log \left (25 e^{-x} x\right )\right ) \int 25^{108+36 x+4 x^2} x \left (e^{-x} x\right )^{108+36 x+4 x^2} \, dx+\left (9216 \log \left (25 e^{-x} x\right )\right ) \int 25^{108+36 x+4 x^2} \left (e^{-x} x\right )^{108+36 x+4 x^2} \, dx\\ &=-\left (1024 \int 25^{108+36 x+4 x^2} x^2 \left (e^{-x} x\right )^{108+36 x+4 x^2} \, dx\right )+2048 \int \left (\int 25^{4 \left (27+9 x+x^2\right )} x \left (e^{-x} x\right )^{4 \left (27+9 x+x^2\right )} \, dx\right ) \, dx-2048 \int \frac {\int 25^{4 \left (27+9 x+x^2\right )} x \left (e^{-x} x\right )^{4 \left (27+9 x+x^2\right )} \, dx}{x} \, dx-8192 \int 25^{108+36 x+4 x^2} x \left (e^{-x} x\right )^{108+36 x+4 x^2} \, dx+9216 \int \left (\int 25^{4 \left (27+9 x+x^2\right )} \left (e^{-x} x\right )^{4 \left (27+9 x+x^2\right )} \, dx\right ) \, dx-9216 \int \frac {\int 25^{4 \left (27+9 x+x^2\right )} \left (e^{-x} x\right )^{4 \left (27+9 x+x^2\right )} \, dx}{x} \, dx-18432 \int 25^{108+36 x+4 x^2} \left (e^{-x} x\right )^{108+36 x+4 x^2} \, dx+27648 \int \frac {25^{108+36 x+4 x^2} \left (e^{-x} x\right )^{108+36 x+4 x^2}}{x} \, dx+\left (2048 \log \left (25 e^{-x} x\right )\right ) \int 25^{108+36 x+4 x^2} x \left (e^{-x} x\right )^{108+36 x+4 x^2} \, dx+\left (9216 \log \left (25 e^{-x} x\right )\right ) \int 25^{108+36 x+4 x^2} \left (e^{-x} x\right )^{108+36 x+4 x^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [F] time = 5.27, size = 72, normalized size = 2.48 \begin {gather*} 256 \int \frac {25^{108+36 x+4 x^2} \left (e^{-x} x\right )^{108+36 x+4 x^2} \left (108-72 x-32 x^2-4 x^3+\left (36 x+8 x^2\right ) \log \left (25 e^{-x} x\right )\right )}{x} \, dx \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.59, size = 24, normalized size = 0.83 \begin {gather*} e^{\left (4 \, {\left (x^{2} + 9 \, x + 27\right )} \log \left (25 \, x e^{\left (-x\right )}\right ) + 8 \, \log \relax (2)\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.31, size = 40, normalized size = 1.38 \begin {gather*} e^{\left (4 \, x^{2} \log \left (25 \, x e^{\left (-x\right )}\right ) + 36 \, x \log \left (25 \, x e^{\left (-x\right )}\right ) + 8 \, \log \relax (2) + 108 \, \log \left (25 \, x e^{\left (-x\right )}\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 0.11, size = 112, normalized size = 3.86
method | result | size |
risch | \(256 \,{\mathrm e}^{2 \left (x^{2}+9 x +27\right ) \left (-i \pi \mathrm {csgn}\left (i x \,{\mathrm e}^{-x}\right )^{3}+i \pi \mathrm {csgn}\left (i x \,{\mathrm e}^{-x}\right )^{2} \mathrm {csgn}\left (i x \right )+i \pi \mathrm {csgn}\left (i x \,{\mathrm e}^{-x}\right )^{2} \mathrm {csgn}\left (i {\mathrm e}^{-x}\right )-i \pi \,\mathrm {csgn}\left (i x \,{\mathrm e}^{-x}\right ) \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i {\mathrm e}^{-x}\right )+2 \ln \relax (x )-2 \ln \left ({\mathrm e}^{x}\right )+4 \ln \relax (5)\right )}\) | \(112\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.56, size = 44, normalized size = 1.52 \begin {gather*} 2430865342914508479353150021007861031480567253406705911367623677652226107045071656712478446533481881623815074044969719579967204481363296508789062500000000 \, x^{108} e^{\left (-4 \, x^{3} + 8 \, x^{2} \log \relax (5) + 4 \, x^{2} \log \relax (x) - 36 \, x^{2} + 72 \, x \log \relax (5) + 36 \, x \log \relax (x) - 108 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.24, size = 42, normalized size = 1.45 \begin {gather*} 256\,5^{8\,x^2+72\,x+216}\,x^{4\,x^2+36\,x+108}\,{\mathrm {e}}^{-108\,x}\,{\mathrm {e}}^{-4\,x^3}\,{\mathrm {e}}^{-36\,x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [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.
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