Integrand size = 127, antiderivative size = 25 \[ \int \left (e^{5 x^3} \left (32-1920 x^2+480 x^3\right )+e^{10 x^3} \left (-128+32 x+7680 x^2-3840 x^3+480 x^4\right )+\left (64 x+e^{5 x^3} \left (-256 x+64 x^2\right )\right ) \log (x)+\left (64 x+e^{5 x^3} \left (-256 x+96 x^2-1920 x^4+480 x^5\right )\right ) \log ^2(x)+64 x^3 \log ^3(x)+64 x^3 \log ^4(x)\right ) \, dx=16 \left (1+e^{5 x^3} (-4+x)+x^2 \log ^2(x)\right )^2 \]
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\[ \int \left (e^{5 x^3} \left (32-1920 x^2+480 x^3\right )+e^{10 x^3} \left (-128+32 x+7680 x^2-3840 x^3+480 x^4\right )+\left (64 x+e^{5 x^3} \left (-256 x+64 x^2\right )\right ) \log (x)+\left (64 x+e^{5 x^3} \left (-256 x+96 x^2-1920 x^4+480 x^5\right )\right ) \log ^2(x)+64 x^3 \log ^3(x)+64 x^3 \log ^4(x)\right ) \, dx=\int \left (e^{5 x^3} \left (32-1920 x^2+480 x^3\right )+e^{10 x^3} \left (-128+32 x+7680 x^2-3840 x^3+480 x^4\right )+\left (64 x+e^{5 x^3} \left (-256 x+64 x^2\right )\right ) \log (x)+\left (64 x+e^{5 x^3} \left (-256 x+96 x^2-1920 x^4+480 x^5\right )\right ) \log ^2(x)+64 x^3 \log ^3(x)+64 x^3 \log ^4(x)\right ) \, dx \]
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Rubi steps \begin{align*} \text {integral}& = 64 \int x^3 \log ^3(x) \, dx+64 \int x^3 \log ^4(x) \, dx+\int e^{5 x^3} \left (32-1920 x^2+480 x^3\right ) \, dx+\int e^{10 x^3} \left (-128+32 x+7680 x^2-3840 x^3+480 x^4\right ) \, dx+\int \left (64 x+e^{5 x^3} \left (-256 x+64 x^2\right )\right ) \log (x) \, dx+\int \left (64 x+e^{5 x^3} \left (-256 x+96 x^2-1920 x^4+480 x^5\right )\right ) \log ^2(x) \, dx \\ & = \frac {64}{15} e^{5 x^3} \log (x)+32 x^2 \log (x)+\frac {256 x^2 \Gamma \left (\frac {2}{3},-5 x^3\right ) \log (x)}{3\ 5^{2/3} \left (-x^3\right )^{2/3}}+16 x^4 \log ^3(x)+16 x^4 \log ^4(x)-48 \int x^3 \log ^2(x) \, dx-64 \int x^3 \log ^3(x) \, dx+\int \left (32 e^{5 x^3}-1920 e^{5 x^3} x^2+480 e^{5 x^3} x^3\right ) \, dx+\int \left (-128 e^{10 x^3}+32 e^{10 x^3} x+7680 e^{10 x^3} x^2-3840 e^{10 x^3} x^3+480 e^{10 x^3} x^4\right ) \, dx-\int \frac {32 \left (2 e^{5 x^3} x+15 x^3-8 \sqrt [3]{5} \sqrt [3]{-x^3} \Gamma \left (\frac {2}{3},-5 x^3\right )\right )}{15 x^2} \, dx+\int \left (64 x \log ^2(x)+32 e^{5 x^3} x \left (-8+3 x-60 x^3+15 x^4\right ) \log ^2(x)\right ) \, dx \\ & = \frac {64}{15} e^{5 x^3} \log (x)+32 x^2 \log (x)+\frac {256 x^2 \Gamma \left (\frac {2}{3},-5 x^3\right ) \log (x)}{3\ 5^{2/3} \left (-x^3\right )^{2/3}}-12 x^4 \log ^2(x)+16 x^4 \log ^4(x)-\frac {32}{15} \int \frac {2 e^{5 x^3} x+15 x^3-8 \sqrt [3]{5} \sqrt [3]{-x^3} \Gamma \left (\frac {2}{3},-5 x^3\right )}{x^2} \, dx+24 \int x^3 \log (x) \, dx+32 \int e^{5 x^3} \, dx+32 \int e^{10 x^3} x \, dx+32 \int e^{5 x^3} x \left (-8+3 x-60 x^3+15 x^4\right ) \log ^2(x) \, dx+48 \int x^3 \log ^2(x) \, dx+64 \int x \log ^2(x) \, dx-128 \int e^{10 x^3} \, dx+480 \int e^{5 x^3} x^3 \, dx+480 \int e^{10 x^3} x^4 \, dx-1920 \int e^{5 x^3} x^2 \, dx-3840 \int e^{10 x^3} x^3 \, dx+7680 \int e^{10 x^3} x^2 \, dx \\ & = -128 e^{5 x^3}+256 e^{10 x^3}-\frac {3 x^4}{2}+\frac {64\ 2^{2/3} x \Gamma \left (\frac {1}{3},-10 x^3\right )}{3 \sqrt [3]{5} \sqrt [3]{-x^3}}-\frac {32 x \Gamma \left (\frac {1}{3},-5 x^3\right )}{3 \sqrt [3]{5} \sqrt [3]{-x^3}}-\frac {16 \sqrt [3]{2} x^2 \Gamma \left (\frac {2}{3},-10 x^3\right )}{3\ 5^{2/3} \left (-x^3\right )^{2/3}}+\frac {64\ 2^{2/3} x^4 \Gamma \left (\frac {4}{3},-10 x^3\right )}{\sqrt [3]{5} \left (-x^3\right )^{4/3}}-\frac {32 x^4 \Gamma \left (\frac {4}{3},-5 x^3\right )}{\sqrt [3]{5} \left (-x^3\right )^{4/3}}-\frac {8 \sqrt [3]{2} x^5 \Gamma \left (\frac {5}{3},-10 x^3\right )}{5^{2/3} \left (-x^3\right )^{5/3}}+\frac {64}{15} e^{5 x^3} \log (x)+32 x^2 \log (x)+6 x^4 \log (x)+\frac {256 x^2 \Gamma \left (\frac {2}{3},-5 x^3\right ) \log (x)}{3\ 5^{2/3} \left (-x^3\right )^{2/3}}+32 x^2 \log ^2(x)+16 x^4 \log ^4(x)-\frac {32}{15} \int \left (\frac {2 e^{5 x^3}}{x}+15 x+\frac {8 \sqrt [3]{5} x \Gamma \left (\frac {2}{3},-5 x^3\right )}{\left (-x^3\right )^{2/3}}\right ) \, dx-24 \int x^3 \log (x) \, dx+32 \int \left (-8 e^{5 x^3} x \log ^2(x)+3 e^{5 x^3} x^2 \log ^2(x)-60 e^{5 x^3} x^4 \log ^2(x)+15 e^{5 x^3} x^5 \log ^2(x)\right ) \, dx-64 \int x \log (x) \, dx \\ & = -128 e^{5 x^3}+256 e^{10 x^3}+\frac {64\ 2^{2/3} x \Gamma \left (\frac {1}{3},-10 x^3\right )}{3 \sqrt [3]{5} \sqrt [3]{-x^3}}-\frac {32 x \Gamma \left (\frac {1}{3},-5 x^3\right )}{3 \sqrt [3]{5} \sqrt [3]{-x^3}}-\frac {16 \sqrt [3]{2} x^2 \Gamma \left (\frac {2}{3},-10 x^3\right )}{3\ 5^{2/3} \left (-x^3\right )^{2/3}}+\frac {64\ 2^{2/3} x^4 \Gamma \left (\frac {4}{3},-10 x^3\right )}{\sqrt [3]{5} \left (-x^3\right )^{4/3}}-\frac {32 x^4 \Gamma \left (\frac {4}{3},-5 x^3\right )}{\sqrt [3]{5} \left (-x^3\right )^{4/3}}-\frac {8 \sqrt [3]{2} x^5 \Gamma \left (\frac {5}{3},-10 x^3\right )}{5^{2/3} \left (-x^3\right )^{5/3}}+\frac {64}{15} e^{5 x^3} \log (x)+\frac {256 x^2 \Gamma \left (\frac {2}{3},-5 x^3\right ) \log (x)}{3\ 5^{2/3} \left (-x^3\right )^{2/3}}+32 x^2 \log ^2(x)+16 x^4 \log ^4(x)-\frac {64}{15} \int \frac {e^{5 x^3}}{x} \, dx+96 \int e^{5 x^3} x^2 \log ^2(x) \, dx-256 \int e^{5 x^3} x \log ^2(x) \, dx+480 \int e^{5 x^3} x^5 \log ^2(x) \, dx-1920 \int e^{5 x^3} x^4 \log ^2(x) \, dx-\frac {256 \int \frac {x \Gamma \left (\frac {2}{3},-5 x^3\right )}{\left (-x^3\right )^{2/3}} \, dx}{3\ 5^{2/3}} \\ & = -128 e^{5 x^3}+256 e^{10 x^3}-\frac {64 \text {Ei}\left (5 x^3\right )}{45}+\frac {64\ 2^{2/3} x \Gamma \left (\frac {1}{3},-10 x^3\right )}{3 \sqrt [3]{5} \sqrt [3]{-x^3}}-\frac {32 x \Gamma \left (\frac {1}{3},-5 x^3\right )}{3 \sqrt [3]{5} \sqrt [3]{-x^3}}-\frac {16 \sqrt [3]{2} x^2 \Gamma \left (\frac {2}{3},-10 x^3\right )}{3\ 5^{2/3} \left (-x^3\right )^{2/3}}+\frac {64\ 2^{2/3} x^4 \Gamma \left (\frac {4}{3},-10 x^3\right )}{\sqrt [3]{5} \left (-x^3\right )^{4/3}}-\frac {32 x^4 \Gamma \left (\frac {4}{3},-5 x^3\right )}{\sqrt [3]{5} \left (-x^3\right )^{4/3}}-\frac {8 \sqrt [3]{2} x^5 \Gamma \left (\frac {5}{3},-10 x^3\right )}{5^{2/3} \left (-x^3\right )^{5/3}}+\frac {64}{15} e^{5 x^3} \log (x)+\frac {256 x^2 \Gamma \left (\frac {2}{3},-5 x^3\right ) \log (x)}{3\ 5^{2/3} \left (-x^3\right )^{2/3}}+32 x^2 \log ^2(x)+16 x^4 \log ^4(x)+96 \int e^{5 x^3} x^2 \log ^2(x) \, dx-256 \int e^{5 x^3} x \log ^2(x) \, dx+480 \int e^{5 x^3} x^5 \log ^2(x) \, dx-1920 \int e^{5 x^3} x^4 \log ^2(x) \, dx-\frac {\left (256 x^2\right ) \int \frac {\Gamma \left (\frac {2}{3},-5 x^3\right )}{x} \, dx}{3\ 5^{2/3} \left (-x^3\right )^{2/3}} \\ & = -128 e^{5 x^3}+256 e^{10 x^3}-\frac {64 \text {Ei}\left (5 x^3\right )}{45}+\frac {64\ 2^{2/3} x \Gamma \left (\frac {1}{3},-10 x^3\right )}{3 \sqrt [3]{5} \sqrt [3]{-x^3}}-\frac {32 x \Gamma \left (\frac {1}{3},-5 x^3\right )}{3 \sqrt [3]{5} \sqrt [3]{-x^3}}-\frac {16 \sqrt [3]{2} x^2 \Gamma \left (\frac {2}{3},-10 x^3\right )}{3\ 5^{2/3} \left (-x^3\right )^{2/3}}+\frac {64\ 2^{2/3} x^4 \Gamma \left (\frac {4}{3},-10 x^3\right )}{\sqrt [3]{5} \left (-x^3\right )^{4/3}}-\frac {32 x^4 \Gamma \left (\frac {4}{3},-5 x^3\right )}{\sqrt [3]{5} \left (-x^3\right )^{4/3}}-\frac {8 \sqrt [3]{2} x^5 \Gamma \left (\frac {5}{3},-10 x^3\right )}{5^{2/3} \left (-x^3\right )^{5/3}}+\frac {64}{15} e^{5 x^3} \log (x)+\frac {256 x^2 \Gamma \left (\frac {2}{3},-5 x^3\right ) \log (x)}{3\ 5^{2/3} \left (-x^3\right )^{2/3}}+32 x^2 \log ^2(x)+16 x^4 \log ^4(x)+96 \int e^{5 x^3} x^2 \log ^2(x) \, dx-256 \int e^{5 x^3} x \log ^2(x) \, dx+480 \int e^{5 x^3} x^5 \log ^2(x) \, dx-1920 \int e^{5 x^3} x^4 \log ^2(x) \, dx-\frac {\left (256 x^2\right ) \text {Subst}\left (\int \frac {\Gamma \left (\frac {2}{3},-5 x\right )}{x} \, dx,x,x^3\right )}{9\ 5^{2/3} \left (-x^3\right )^{2/3}} \\ & = -128 e^{5 x^3}+256 e^{10 x^3}-\frac {64 \text {Ei}\left (5 x^3\right )}{45}+\frac {64\ 2^{2/3} x \Gamma \left (\frac {1}{3},-10 x^3\right )}{3 \sqrt [3]{5} \sqrt [3]{-x^3}}-\frac {32 x \Gamma \left (\frac {1}{3},-5 x^3\right )}{3 \sqrt [3]{5} \sqrt [3]{-x^3}}-\frac {16 \sqrt [3]{2} x^2 \Gamma \left (\frac {2}{3},-10 x^3\right )}{3\ 5^{2/3} \left (-x^3\right )^{2/3}}+\frac {64\ 2^{2/3} x^4 \Gamma \left (\frac {4}{3},-10 x^3\right )}{\sqrt [3]{5} \left (-x^3\right )^{4/3}}-\frac {32 x^4 \Gamma \left (\frac {4}{3},-5 x^3\right )}{\sqrt [3]{5} \left (-x^3\right )^{4/3}}-\frac {8 \sqrt [3]{2} x^5 \Gamma \left (\frac {5}{3},-10 x^3\right )}{5^{2/3} \left (-x^3\right )^{5/3}}+64 x^2 \, _2F_2\left (\frac {2}{3},\frac {2}{3};\frac {5}{3},\frac {5}{3};5 x^3\right )+\frac {64}{15} e^{5 x^3} \log (x)-\frac {256 x^2 \Gamma \left (\frac {2}{3}\right ) \log (x)}{3\ 5^{2/3} \left (-x^3\right )^{2/3}}+\frac {256 x^2 \Gamma \left (\frac {2}{3},-5 x^3\right ) \log (x)}{3\ 5^{2/3} \left (-x^3\right )^{2/3}}+32 x^2 \log ^2(x)+16 x^4 \log ^4(x)+96 \int e^{5 x^3} x^2 \log ^2(x) \, dx-256 \int e^{5 x^3} x \log ^2(x) \, dx+480 \int e^{5 x^3} x^5 \log ^2(x) \, dx-1920 \int e^{5 x^3} x^4 \log ^2(x) \, dx \\ \end{align*}
Result contains higher order function than in optimal. Order 5 vs. order 3 in optimal.
Time = 0.78 (sec) , antiderivative size = 316, normalized size of antiderivative = 12.64 \[ \int \left (e^{5 x^3} \left (32-1920 x^2+480 x^3\right )+e^{10 x^3} \left (-128+32 x+7680 x^2-3840 x^3+480 x^4\right )+\left (64 x+e^{5 x^3} \left (-256 x+64 x^2\right )\right ) \log (x)+\left (64 x+e^{5 x^3} \left (-256 x+96 x^2-1920 x^4+480 x^5\right )\right ) \log ^2(x)+64 x^3 \log ^3(x)+64 x^3 \log ^4(x)\right ) \, dx=32 \left (\frac {1}{2}-4 e^{5 x^3}+8 e^{10 x^3}+e^{5 x^3} x-4 e^{10 x^3} x+\frac {1}{2} e^{10 x^3} x^2-2 x^2 \, _3F_3\left (\frac {2}{3},\frac {2}{3},\frac {2}{3};\frac {5}{3},\frac {5}{3},\frac {5}{3};5 x^3\right )-\frac {24}{25} x^5 \, _3F_3\left (\frac {5}{3},\frac {5}{3},\frac {5}{3};\frac {8}{3},\frac {8}{3},\frac {8}{3};5 x^3\right )+\frac {8 \sqrt [3]{-x^3} \Gamma \left (\frac {2}{3},0,-5 x^3\right ) \log (x)}{3\ 5^{2/3} x}+\frac {24}{5} x^5 \, _2F_2\left (\frac {5}{3},\frac {5}{3};\frac {8}{3},\frac {8}{3};5 x^3\right ) \log (x)+x^2 \log ^2(x)+e^{5 x^3} x^3 \log ^2(x)+\frac {8 \sqrt [3]{-x^3} \Gamma \left (\frac {2}{3},0,-5 x^3\right ) \log ^2(x)}{3\ 5^{2/3} x}+\frac {4 x^2 \Gamma \left (\frac {5}{3},0,-5 x^3\right ) \log ^2(x)}{5^{2/3} \left (-x^3\right )^{2/3}}+\frac {1}{2} x^4 \log ^4(x)+2 x^2 \, _2F_2\left (\frac {2}{3},\frac {2}{3};\frac {5}{3},\frac {5}{3};5 x^3\right ) (1+2 \log (x))\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. \(74\) vs. \(2(24)=48\).
Time = 0.21 (sec) , antiderivative size = 75, normalized size of antiderivative = 3.00
method | result | size |
risch | \(16 x^{4} \ln \left (x \right )^{4}+\left (16 x^{2}-128 x +256\right ) {\mathrm e}^{10 x^{3}}+\left (32 x -128\right ) {\mathrm e}^{5 x^{3}}+\left (32 \,{\mathrm e}^{5 x^{3}} x^{3}-128 x^{2} {\mathrm e}^{5 x^{3}}+32 x^{2}\right ) \ln \left (x \right )^{2}\) | \(75\) |
parallelrisch | \(16 x^{4} \ln \left (x \right )^{4}+32 \,{\mathrm e}^{5 x^{3}} \ln \left (x \right )^{2} x^{3}-128 \,{\mathrm e}^{5 x^{3}} \ln \left (x \right )^{2} x^{2}+32 x^{2} \ln \left (x \right )^{2}+16 \,{\mathrm e}^{10 x^{3}} x^{2}+32 \,{\mathrm e}^{5 x^{3}} x -128 \,{\mathrm e}^{10 x^{3}} x -128 \,{\mathrm e}^{5 x^{3}}+256 \,{\mathrm e}^{10 x^{3}}\) | \(101\) |
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Leaf count of result is larger than twice the leaf count of optimal. 63 vs. \(2 (24) = 48\).
Time = 0.23 (sec) , antiderivative size = 63, normalized size of antiderivative = 2.52 \[ \int \left (e^{5 x^3} \left (32-1920 x^2+480 x^3\right )+e^{10 x^3} \left (-128+32 x+7680 x^2-3840 x^3+480 x^4\right )+\left (64 x+e^{5 x^3} \left (-256 x+64 x^2\right )\right ) \log (x)+\left (64 x+e^{5 x^3} \left (-256 x+96 x^2-1920 x^4+480 x^5\right )\right ) \log ^2(x)+64 x^3 \log ^3(x)+64 x^3 \log ^4(x)\right ) \, dx=16 \, x^{4} \log \left (x\right )^{4} + 32 \, {\left (x^{2} + {\left (x^{3} - 4 \, x^{2}\right )} e^{\left (5 \, x^{3}\right )}\right )} \log \left (x\right )^{2} + 16 \, {\left (x^{2} - 8 \, x + 16\right )} e^{\left (10 \, x^{3}\right )} + 32 \, {\left (x - 4\right )} e^{\left (5 \, x^{3}\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 68 vs. \(2 (22) = 44\).
Time = 0.21 (sec) , antiderivative size = 68, normalized size of antiderivative = 2.72 \[ \int \left (e^{5 x^3} \left (32-1920 x^2+480 x^3\right )+e^{10 x^3} \left (-128+32 x+7680 x^2-3840 x^3+480 x^4\right )+\left (64 x+e^{5 x^3} \left (-256 x+64 x^2\right )\right ) \log (x)+\left (64 x+e^{5 x^3} \left (-256 x+96 x^2-1920 x^4+480 x^5\right )\right ) \log ^2(x)+64 x^3 \log ^3(x)+64 x^3 \log ^4(x)\right ) \, dx=16 x^{4} \log {\left (x \right )}^{4} + 32 x^{2} \log {\left (x \right )}^{2} + \left (16 x^{2} - 128 x + 256\right ) e^{10 x^{3}} + \left (32 x^{3} \log {\left (x \right )}^{2} - 128 x^{2} \log {\left (x \right )}^{2} + 32 x - 128\right ) e^{5 x^{3}} \]
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Result contains higher order function than in optimal. Order 4 vs. order 3.
Time = 0.23 (sec) , antiderivative size = 106, normalized size of antiderivative = 4.24 \[ \int \left (e^{5 x^3} \left (32-1920 x^2+480 x^3\right )+e^{10 x^3} \left (-128+32 x+7680 x^2-3840 x^3+480 x^4\right )+\left (64 x+e^{5 x^3} \left (-256 x+64 x^2\right )\right ) \log (x)+\left (64 x+e^{5 x^3} \left (-256 x+96 x^2-1920 x^4+480 x^5\right )\right ) \log ^2(x)+64 x^3 \log ^3(x)+64 x^3 \log ^4(x)\right ) \, dx=16 \, x^{4} \log \left (x\right )^{4} - \frac {32 \cdot 5^{\frac {2}{3}} x^{4} \Gamma \left (\frac {4}{3}, -5 \, x^{3}\right )}{5 \, \left (-x^{3}\right )^{\frac {4}{3}}} + 32 \, x^{2} \log \left (x\right )^{2} + 32 \, {\left (x^{3} - 4 \, x^{2}\right )} e^{\left (5 \, x^{3}\right )} \log \left (x\right )^{2} - \frac {32 \cdot 5^{\frac {2}{3}} x \Gamma \left (\frac {1}{3}, -5 \, x^{3}\right )}{15 \, \left (-x^{3}\right )^{\frac {1}{3}}} + 16 \, {\left (x^{2} - 8 \, x + 16\right )} e^{\left (10 \, x^{3}\right )} - 128 \, e^{\left (5 \, x^{3}\right )} \]
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\[ \int \left (e^{5 x^3} \left (32-1920 x^2+480 x^3\right )+e^{10 x^3} \left (-128+32 x+7680 x^2-3840 x^3+480 x^4\right )+\left (64 x+e^{5 x^3} \left (-256 x+64 x^2\right )\right ) \log (x)+\left (64 x+e^{5 x^3} \left (-256 x+96 x^2-1920 x^4+480 x^5\right )\right ) \log ^2(x)+64 x^3 \log ^3(x)+64 x^3 \log ^4(x)\right ) \, dx=\int { 64 \, x^{3} \log \left (x\right )^{4} + 64 \, x^{3} \log \left (x\right )^{3} + 32 \, {\left ({\left (15 \, x^{5} - 60 \, x^{4} + 3 \, x^{2} - 8 \, x\right )} e^{\left (5 \, x^{3}\right )} + 2 \, x\right )} \log \left (x\right )^{2} + 32 \, {\left (15 \, x^{4} - 120 \, x^{3} + 240 \, x^{2} + x - 4\right )} e^{\left (10 \, x^{3}\right )} + 32 \, {\left (15 \, x^{3} - 60 \, x^{2} + 1\right )} e^{\left (5 \, x^{3}\right )} + 64 \, {\left ({\left (x^{2} - 4 \, x\right )} e^{\left (5 \, x^{3}\right )} + x\right )} \log \left (x\right ) \,d x } \]
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Timed out. \[ \int \left (e^{5 x^3} \left (32-1920 x^2+480 x^3\right )+e^{10 x^3} \left (-128+32 x+7680 x^2-3840 x^3+480 x^4\right )+\left (64 x+e^{5 x^3} \left (-256 x+64 x^2\right )\right ) \log (x)+\left (64 x+e^{5 x^3} \left (-256 x+96 x^2-1920 x^4+480 x^5\right )\right ) \log ^2(x)+64 x^3 \log ^3(x)+64 x^3 \log ^4(x)\right ) \, dx=\int 64\,x^3\,{\ln \left (x\right )}^3+64\,x^3\,{\ln \left (x\right )}^4+{\ln \left (x\right )}^2\,\left (64\,x-{\mathrm {e}}^{5\,x^3}\,\left (-480\,x^5+1920\,x^4-96\,x^2+256\,x\right )\right )+{\mathrm {e}}^{5\,x^3}\,\left (480\,x^3-1920\,x^2+32\right )+{\mathrm {e}}^{10\,x^3}\,\left (480\,x^4-3840\,x^3+7680\,x^2+32\,x-128\right )+\ln \left (x\right )\,\left (64\,x-{\mathrm {e}}^{5\,x^3}\,\left (256\,x-64\,x^2\right )\right ) \,d x \]
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