Optimal. Leaf size=27 \[ \left (2-e^{8+\frac {3 x}{5}}+x\right )^4 \left (\frac {4}{x}+\log ^2(x)\right ) \]
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Rubi [F] time = 4.68, 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 {-320+480 x^2+320 x^3+60 x^4+e^{\frac {4}{5} (40+3 x)} (-20+48 x)+e^{\frac {3}{5} (40+3 x)} \left (160-288 x-144 x^2\right )+e^{\frac {2}{5} (40+3 x)} \left (-480+576 x+696 x^2+144 x^3\right )+e^{\frac {1}{5} (40+3 x)} \left (640-384 x-1056 x^2-448 x^3-48 x^4\right )+\left (160 x+10 e^{\frac {4}{5} (40+3 x)} x+320 x^2+240 x^3+80 x^4+10 x^5+e^{\frac {3}{5} (40+3 x)} \left (-80 x-40 x^2\right )+e^{\frac {2}{5} (40+3 x)} \left (240 x+240 x^2+60 x^3\right )+e^{\frac {1}{5} (40+3 x)} \left (-320 x-480 x^2-240 x^3-40 x^4\right )\right ) \log (x)+\left (160 x^2+12 e^{\frac {4}{5} (40+3 x)} x^2+240 x^3+120 x^4+20 x^5+e^{\frac {3}{5} (40+3 x)} \left (-92 x^2-36 x^3\right )+e^{\frac {2}{5} (40+3 x)} \left (264 x^2+204 x^3+36 x^4\right )+e^{\frac {1}{5} (40+3 x)} \left (-336 x^2-384 x^3-132 x^4-12 x^5\right )\right ) \log ^2(x)}{5 x^2} \, dx \end {gather*}
Verification is not applicable to the result.
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\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int \frac {-320+480 x^2+320 x^3+60 x^4+e^{\frac {4}{5} (40+3 x)} (-20+48 x)+e^{\frac {3}{5} (40+3 x)} \left (160-288 x-144 x^2\right )+e^{\frac {2}{5} (40+3 x)} \left (-480+576 x+696 x^2+144 x^3\right )+e^{\frac {1}{5} (40+3 x)} \left (640-384 x-1056 x^2-448 x^3-48 x^4\right )+\left (160 x+10 e^{\frac {4}{5} (40+3 x)} x+320 x^2+240 x^3+80 x^4+10 x^5+e^{\frac {3}{5} (40+3 x)} \left (-80 x-40 x^2\right )+e^{\frac {2}{5} (40+3 x)} \left (240 x+240 x^2+60 x^3\right )+e^{\frac {1}{5} (40+3 x)} \left (-320 x-480 x^2-240 x^3-40 x^4\right )\right ) \log (x)+\left (160 x^2+12 e^{\frac {4}{5} (40+3 x)} x^2+240 x^3+120 x^4+20 x^5+e^{\frac {3}{5} (40+3 x)} \left (-92 x^2-36 x^3\right )+e^{\frac {2}{5} (40+3 x)} \left (264 x^2+204 x^3+36 x^4\right )+e^{\frac {1}{5} (40+3 x)} \left (-336 x^2-384 x^3-132 x^4-12 x^5\right )\right ) \log ^2(x)}{x^2} \, dx\\ &=\frac {1}{5} \int \left (\frac {10 (2+x)^3 \left (-4+6 x+2 x \log (x)+x^2 \log (x)+2 x^2 \log ^2(x)\right )}{x^2}+\frac {2 e^{32+\frac {12 x}{5}} \left (-10+24 x+5 x \log (x)+6 x^2 \log ^2(x)\right )}{x^2}+\frac {12 e^{16+\frac {6 x}{5}} (2+x) \left (-20+34 x+12 x^2+10 x \log (x)+5 x^2 \log (x)+11 x^2 \log ^2(x)+3 x^3 \log ^2(x)\right )}{x^2}-\frac {4 e^{8+\frac {3 x}{5}} (2+x)^2 \left (-40+64 x+12 x^2+20 x \log (x)+10 x^2 \log (x)+21 x^2 \log ^2(x)+3 x^3 \log ^2(x)\right )}{x^2}-\frac {4 e^{24+\frac {9 x}{5}} \left (-40+72 x+36 x^2+20 x \log (x)+10 x^2 \log (x)+23 x^2 \log ^2(x)+9 x^3 \log ^2(x)\right )}{x^2}\right ) \, dx\\ &=\frac {2}{5} \int \frac {e^{32+\frac {12 x}{5}} \left (-10+24 x+5 x \log (x)+6 x^2 \log ^2(x)\right )}{x^2} \, dx-\frac {4}{5} \int \frac {e^{8+\frac {3 x}{5}} (2+x)^2 \left (-40+64 x+12 x^2+20 x \log (x)+10 x^2 \log (x)+21 x^2 \log ^2(x)+3 x^3 \log ^2(x)\right )}{x^2} \, dx-\frac {4}{5} \int \frac {e^{24+\frac {9 x}{5}} \left (-40+72 x+36 x^2+20 x \log (x)+10 x^2 \log (x)+23 x^2 \log ^2(x)+9 x^3 \log ^2(x)\right )}{x^2} \, dx+2 \int \frac {(2+x)^3 \left (-4+6 x+2 x \log (x)+x^2 \log (x)+2 x^2 \log ^2(x)\right )}{x^2} \, dx+\frac {12}{5} \int \frac {e^{16+\frac {6 x}{5}} (2+x) \left (-20+34 x+12 x^2+10 x \log (x)+5 x^2 \log (x)+11 x^2 \log ^2(x)+3 x^3 \log ^2(x)\right )}{x^2} \, dx\\ &=\frac {e^{32+\frac {12 x}{5}} \left (4 x+x^2 \log ^2(x)\right )}{x^2}-\frac {4}{5} \int \left (\frac {4 e^{8+\frac {3 x}{5}} (2+x)^2 \left (-10+16 x+3 x^2\right )}{x^2}+\frac {10 e^{8+\frac {3 x}{5}} (2+x)^3 \log (x)}{x}+3 e^{8+\frac {3 x}{5}} (2+x)^2 (7+x) \log ^2(x)\right ) \, dx-\frac {4}{5} \int \left (\frac {4 e^{24+\frac {9 x}{5}} \left (-10+18 x+9 x^2\right )}{x^2}+\frac {10 e^{24+\frac {9 x}{5}} (2+x) \log (x)}{x}+e^{24+\frac {9 x}{5}} (23+9 x) \log ^2(x)\right ) \, dx+2 \int \left (\frac {2 (2+x)^3 (-2+3 x)}{x^2}+\frac {(2+x)^4 \log (x)}{x}+2 (2+x)^3 \log ^2(x)\right ) \, dx+\frac {12}{5} \int \left (\frac {2 e^{16+\frac {6 x}{5}} (2+x) \left (-10+17 x+6 x^2\right )}{x^2}+\frac {5 e^{16+\frac {6 x}{5}} (2+x)^2 \log (x)}{x}+e^{16+\frac {6 x}{5}} \left (22+17 x+3 x^2\right ) \log ^2(x)\right ) \, dx\\ &=\frac {e^{32+\frac {12 x}{5}} \left (4 x+x^2 \log ^2(x)\right )}{x^2}-\frac {4}{5} \int e^{24+\frac {9 x}{5}} (23+9 x) \log ^2(x) \, dx+2 \int \frac {(2+x)^4 \log (x)}{x} \, dx-\frac {12}{5} \int e^{8+\frac {3 x}{5}} (2+x)^2 (7+x) \log ^2(x) \, dx+\frac {12}{5} \int e^{16+\frac {6 x}{5}} \left (22+17 x+3 x^2\right ) \log ^2(x) \, dx-\frac {16}{5} \int \frac {e^{8+\frac {3 x}{5}} (2+x)^2 \left (-10+16 x+3 x^2\right )}{x^2} \, dx-\frac {16}{5} \int \frac {e^{24+\frac {9 x}{5}} \left (-10+18 x+9 x^2\right )}{x^2} \, dx+4 \int \frac {(2+x)^3 (-2+3 x)}{x^2} \, dx+4 \int (2+x)^3 \log ^2(x) \, dx+\frac {24}{5} \int \frac {e^{16+\frac {6 x}{5}} (2+x) \left (-10+17 x+6 x^2\right )}{x^2} \, dx-8 \int \frac {e^{24+\frac {9 x}{5}} (2+x) \log (x)}{x} \, dx-8 \int \frac {e^{8+\frac {3 x}{5}} (2+x)^3 \log (x)}{x} \, dx+12 \int \frac {e^{16+\frac {6 x}{5}} (2+x)^2 \log (x)}{x} \, dx\\ &=\frac {4 (2+x)^4}{x}-\frac {2720}{27} e^{8+\frac {3 x}{5}} \log (x)+\frac {95}{3} e^{16+\frac {6 x}{5}} \log (x)-\frac {40}{9} e^{24+\frac {9 x}{5}} \log (x)-\frac {320}{9} e^{8+\frac {3 x}{5}} x \log (x)+10 e^{16+\frac {6 x}{5}} x \log (x)-\frac {40}{3} e^{8+\frac {3 x}{5}} x^2 \log (x)-64 e^8 \text {Ei}\left (\frac {3 x}{5}\right ) \log (x)+48 e^{16} \text {Ei}\left (\frac {6 x}{5}\right ) \log (x)-16 e^{24} \text {Ei}\left (\frac {9 x}{5}\right ) \log (x)+(2+x)^4 \log ^2(x)+\frac {1}{6} \log (x) \left (384 x+144 x^2+32 x^3+3 x^4+192 \log (x)\right )+\frac {e^{32+\frac {12 x}{5}} \left (4 x+x^2 \log ^2(x)\right )}{x^2}-\frac {4}{5} \int \left (23 e^{24+\frac {9 x}{5}} \log ^2(x)+9 e^{24+\frac {9 x}{5}} x \log ^2(x)\right ) \, dx-2 \int \frac {(2+x)^4 \log (x)}{x} \, dx-2 \int \left (32+12 x+\frac {8 x^2}{3}+\frac {x^3}{4}+\frac {16 \log (x)}{x}\right ) \, dx+\frac {12}{5} \int \left (22 e^{16+\frac {6 x}{5}} \log ^2(x)+17 e^{16+\frac {6 x}{5}} x \log ^2(x)+3 e^{16+\frac {6 x}{5}} x^2 \log ^2(x)\right ) \, dx-\frac {12}{5} \int \left (28 e^{8+\frac {3 x}{5}} \log ^2(x)+32 e^{8+\frac {3 x}{5}} x \log ^2(x)+11 e^{8+\frac {3 x}{5}} x^2 \log ^2(x)+e^{8+\frac {3 x}{5}} x^3 \log ^2(x)\right ) \, dx-\frac {16}{5} \int \left (9 e^{24+\frac {9 x}{5}}-\frac {10 e^{24+\frac {9 x}{5}}}{x^2}+\frac {18 e^{24+\frac {9 x}{5}}}{x}\right ) \, dx-\frac {16}{5} \int \left (66 e^{8+\frac {3 x}{5}}-\frac {40 e^{8+\frac {3 x}{5}}}{x^2}+\frac {24 e^{8+\frac {3 x}{5}}}{x}+28 e^{8+\frac {3 x}{5}} x+3 e^{8+\frac {3 x}{5}} x^2\right ) \, dx+\frac {24}{5} \int \left (29 e^{16+\frac {6 x}{5}}-\frac {20 e^{16+\frac {6 x}{5}}}{x^2}+\frac {24 e^{16+\frac {6 x}{5}}}{x}+6 e^{16+\frac {6 x}{5}} x\right ) \, dx+8 \int \frac {e^8 \left (5 e^{3 x/5} \left (68+24 x+9 x^2\right )+216 \text {Ei}\left (\frac {3 x}{5}\right )\right )}{27 x} \, dx+8 \int \frac {e^{24} \left (5 e^{9 x/5}+18 \text {Ei}\left (\frac {9 x}{5}\right )\right )}{9 x} \, dx-12 \int \frac {e^{16} \left (5 e^{6 x/5} (19+6 x)+144 \text {Ei}\left (\frac {6 x}{5}\right )\right )}{36 x} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [B] time = 0.24, size = 104, normalized size = 3.85 \begin {gather*} \frac {2}{5} \left (\frac {10 \left (16+e^{32+\frac {12 x}{5}}+24 x^2+8 x^3+x^4-4 e^{24+\frac {9 x}{5}} (2+x)+6 e^{16+\frac {6 x}{5}} (2+x)^2-4 e^{8+\frac {3 x}{5}} (2+x)^3\right )}{x}+\frac {5}{2} \left (2-e^{8+\frac {3 x}{5}}+x\right )^4 \log ^2(x)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.63, size = 172, normalized size = 6.37 \begin {gather*} \frac {4 \, x^{4} + 32 \, x^{3} + {\left (x^{5} + 8 \, x^{4} + 24 \, x^{3} + 32 \, x^{2} + x e^{\left (\frac {12}{5} \, x + 32\right )} - 4 \, {\left (x^{2} + 2 \, x\right )} e^{\left (\frac {9}{5} \, x + 24\right )} + 6 \, {\left (x^{3} + 4 \, x^{2} + 4 \, x\right )} e^{\left (\frac {6}{5} \, x + 16\right )} - 4 \, {\left (x^{4} + 6 \, x^{3} + 12 \, x^{2} + 8 \, x\right )} e^{\left (\frac {3}{5} \, x + 8\right )} + 16 \, x\right )} \log \relax (x)^{2} + 96 \, x^{2} - 16 \, {\left (x + 2\right )} e^{\left (\frac {9}{5} \, x + 24\right )} + 24 \, {\left (x^{2} + 4 \, x + 4\right )} e^{\left (\frac {6}{5} \, x + 16\right )} - 16 \, {\left (x^{3} + 6 \, x^{2} + 12 \, x + 8\right )} e^{\left (\frac {3}{5} \, x + 8\right )} + 4 \, e^{\left (\frac {12}{5} \, x + 32\right )} + 64}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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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.
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maple [B] time = 0.12, size = 230, normalized size = 8.52
method | result | size |
risch | \(\frac {\left (5 x^{4}-20 \,{\mathrm e}^{\frac {3 x}{5}+8} x^{3}+30 \,{\mathrm e}^{\frac {6 x}{5}+16} x^{2}-20 \,{\mathrm e}^{\frac {9 x}{5}+24} x +5 \,{\mathrm e}^{\frac {12 x}{5}+32}+40 x^{3}-120 \,{\mathrm e}^{\frac {3 x}{5}+8} x^{2}+120 \,{\mathrm e}^{\frac {6 x}{5}+16} x -40 \,{\mathrm e}^{\frac {9 x}{5}+24}+120 x^{2}-240 \,{\mathrm e}^{\frac {3 x}{5}+8} x +120 \,{\mathrm e}^{\frac {6 x}{5}+16}+160 x -160 \,{\mathrm e}^{\frac {3 x}{5}+8}+80\right ) \ln \relax (x )^{2}}{5}+\frac {4 x^{4}-16 \,{\mathrm e}^{\frac {3 x}{5}+8} x^{3}+24 \,{\mathrm e}^{\frac {6 x}{5}+16} x^{2}-16 \,{\mathrm e}^{\frac {9 x}{5}+24} x +4 \,{\mathrm e}^{\frac {12 x}{5}+32}+32 x^{3}-96 \,{\mathrm e}^{\frac {3 x}{5}+8} x^{2}+96 \,{\mathrm e}^{\frac {6 x}{5}+16} x -32 \,{\mathrm e}^{\frac {9 x}{5}+24}+96 x^{2}-192 \,{\mathrm e}^{\frac {3 x}{5}+8} x +96 \,{\mathrm e}^{\frac {6 x}{5}+16}-128 \,{\mathrm e}^{\frac {3 x}{5}+8}+64}{x}\) | \(230\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \frac {1}{2} \, x^{4} \log \relax (x) + \frac {16}{3} \, x^{3} \log \relax (x) - 4 \, {\left (x e^{24} + 2 \, e^{24}\right )} e^{\left (\frac {9}{5} \, x\right )} \log \relax (x)^{2} + 6 \, {\left (x^{2} e^{16} + 4 \, x e^{16} + 4 \, e^{16}\right )} e^{\left (\frac {6}{5} \, x\right )} \log \relax (x)^{2} + 4 \, x^{3} + 24 \, x^{2} \log \relax (x) + {\left (x^{4} + 8 \, x^{3} + 24 \, x^{2} + 32 \, x\right )} \log \relax (x)^{2} + e^{\left (\frac {12}{5} \, x + 32\right )} \log \relax (x)^{2} + 32 \, x^{2} + \frac {48}{5} \, {\rm Ei}\left (\frac {12}{5} \, x\right ) e^{32} - \frac {288}{5} \, {\rm Ei}\left (\frac {9}{5} \, x\right ) e^{24} + \frac {576}{5} \, {\rm Ei}\left (\frac {6}{5} \, x\right ) e^{16} + \frac {416}{5} \, {\rm Ei}\left (\frac {3}{5} \, x\right ) e^{8} + 4 \, {\left (6 \, x e^{16} - 5 \, e^{16}\right )} e^{\left (\frac {6}{5} \, x\right )} - \frac {16}{9} \, {\left (9 \, x^{2} e^{8} - 30 \, x e^{8} + 50 \, e^{8}\right )} e^{\left (\frac {3}{5} \, x\right )} - 4 \, {\left ({\left (x^{3} e^{8} + 6 \, x^{2} e^{8} + 12 \, x e^{8} + 8 \, e^{8}\right )} \log \relax (x)^{2} - 40 \, e^{8} \log \relax (x)\right )} e^{\left (\frac {3}{5} \, x\right )} - \frac {448}{9} \, {\left (3 \, x e^{8} - 5 \, e^{8}\right )} e^{\left (\frac {3}{5} \, x\right )} + \frac {384}{5} \, e^{8} \Gamma \left (-1, -\frac {3}{5} \, x\right ) - \frac {576}{5} \, e^{16} \Gamma \left (-1, -\frac {6}{5} \, x\right ) + \frac {288}{5} \, e^{24} \Gamma \left (-1, -\frac {9}{5} \, x\right ) - \frac {48}{5} \, e^{32} \Gamma \left (-1, -\frac {12}{5} \, x\right ) - \frac {1}{6} \, {\left (3 \, x^{4} + 32 \, x^{3} + 144 \, x^{2} + 384 \, x\right )} \log \relax (x) + 64 \, x \log \relax (x) - 160 \, e^{\left (\frac {3}{5} \, x + 8\right )} \log \relax (x) + 16 \, \log \relax (x)^{2} + 96 \, x + \frac {64}{x} - 16 \, e^{\left (\frac {9}{5} \, x + 24\right )} + 116 \, e^{\left (\frac {6}{5} \, x + 16\right )} - 352 \, e^{\left (\frac {3}{5} \, x + 8\right )} - 160 \, \int \frac {e^{\left (\frac {3}{5} \, x + 8\right )}}{x}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {\frac {{\mathrm {e}}^{\frac {12\,x}{5}+32}\,\left (48\,x-20\right )}{5}-\frac {{\mathrm {e}}^{\frac {9\,x}{5}+24}\,\left (144\,x^2+288\,x-160\right )}{5}+\frac {{\mathrm {e}}^{\frac {6\,x}{5}+16}\,\left (144\,x^3+696\,x^2+576\,x-480\right )}{5}+\frac {\ln \relax (x)\,\left (160\,x-{\mathrm {e}}^{\frac {9\,x}{5}+24}\,\left (40\,x^2+80\,x\right )+10\,x\,{\mathrm {e}}^{\frac {12\,x}{5}+32}+{\mathrm {e}}^{\frac {6\,x}{5}+16}\,\left (60\,x^3+240\,x^2+240\,x\right )-{\mathrm {e}}^{\frac {3\,x}{5}+8}\,\left (40\,x^4+240\,x^3+480\,x^2+320\,x\right )+320\,x^2+240\,x^3+80\,x^4+10\,x^5\right )}{5}+\frac {{\ln \relax (x)}^2\,\left (12\,x^2\,{\mathrm {e}}^{\frac {12\,x}{5}+32}-{\mathrm {e}}^{\frac {9\,x}{5}+24}\,\left (36\,x^3+92\,x^2\right )-{\mathrm {e}}^{\frac {3\,x}{5}+8}\,\left (12\,x^5+132\,x^4+384\,x^3+336\,x^2\right )+160\,x^2+240\,x^3+120\,x^4+20\,x^5+{\mathrm {e}}^{\frac {6\,x}{5}+16}\,\left (36\,x^4+204\,x^3+264\,x^2\right )\right )}{5}-\frac {{\mathrm {e}}^{\frac {3\,x}{5}+8}\,\left (48\,x^4+448\,x^3+1056\,x^2+384\,x-640\right )}{5}+96\,x^2+64\,x^3+12\,x^4-64}{x^2} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.81, size = 231, normalized size = 8.56 \begin {gather*} 4 x^{3} + 32 x^{2} + 96 x + \left (x^{4} + 8 x^{3} + 24 x^{2} + 32 x + 16\right ) \log {\relax (x )}^{2} + \frac {64}{x} + \frac {\left (x^{4} \log {\relax (x )}^{2} + 4 x^{3}\right ) e^{\frac {12 x}{5} + 32} + \left (- 4 x^{5} \log {\relax (x )}^{2} - 8 x^{4} \log {\relax (x )}^{2} - 16 x^{4} - 32 x^{3}\right ) e^{\frac {9 x}{5} + 24} + \left (6 x^{6} \log {\relax (x )}^{2} + 24 x^{5} \log {\relax (x )}^{2} + 24 x^{5} + 24 x^{4} \log {\relax (x )}^{2} + 96 x^{4} + 96 x^{3}\right ) e^{\frac {6 x}{5} + 16} + \left (- 4 x^{7} \log {\relax (x )}^{2} - 24 x^{6} \log {\relax (x )}^{2} - 16 x^{6} - 48 x^{5} \log {\relax (x )}^{2} - 96 x^{5} - 32 x^{4} \log {\relax (x )}^{2} - 192 x^{4} - 128 x^{3}\right ) e^{\frac {3 x}{5} + 8}}{x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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