Integrand size = 109, antiderivative size = 35 \[ \int \frac {60+60 x+e^x \left (-16+24 x-9 x^2\right )+e^{x+e^x x} \left (16-8 x-15 x^2+9 x^3+e^x \left (16+8 x-23 x^2-6 x^3+9 x^4\right )\right )+e^x \left (-16+8 x+15 x^2-9 x^3\right ) \log (1+x)}{16-8 x-15 x^2+9 x^3} \, dx=4+e^{x+e^x x}+\frac {5}{-x+\frac {4+x}{4}}-e^x \log (1+x) \]
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\[ \int \frac {60+60 x+e^x \left (-16+24 x-9 x^2\right )+e^{x+e^x x} \left (16-8 x-15 x^2+9 x^3+e^x \left (16+8 x-23 x^2-6 x^3+9 x^4\right )\right )+e^x \left (-16+8 x+15 x^2-9 x^3\right ) \log (1+x)}{16-8 x-15 x^2+9 x^3} \, dx=\int \frac {60+60 x+e^x \left (-16+24 x-9 x^2\right )+e^{x+e^x x} \left (16-8 x-15 x^2+9 x^3+e^x \left (16+8 x-23 x^2-6 x^3+9 x^4\right )\right )+e^x \left (-16+8 x+15 x^2-9 x^3\right ) \log (1+x)}{16-8 x-15 x^2+9 x^3} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \left (e^{x+e^x x}+\frac {60}{(4-3 x)^2}-\frac {e^x}{1+x}+e^{2 x+e^x x} (1+x)-e^x \log (1+x)\right ) \, dx \\ & = \frac {20}{4-3 x}+\int e^{x+e^x x} \, dx-\int \frac {e^x}{1+x} \, dx+\int e^{2 x+e^x x} (1+x) \, dx-\int e^x \log (1+x) \, dx \\ & = \frac {20}{4-3 x}-\frac {\operatorname {ExpIntegralEi}(1+x)}{e}-e^x \log (1+x)+\int e^{x+e^x x} \, dx+\int \frac {e^x}{1+x} \, dx+\int \left (e^{2 x+e^x x}+e^{2 x+e^x x} x\right ) \, dx \\ & = \frac {20}{4-3 x}-e^x \log (1+x)+\int e^{x+e^x x} \, dx+\int e^{2 x+e^x x} \, dx+\int e^{2 x+e^x x} x \, dx \\ \end{align*}
Time = 0.25 (sec) , antiderivative size = 28, normalized size of antiderivative = 0.80 \[ \int \frac {60+60 x+e^x \left (-16+24 x-9 x^2\right )+e^{x+e^x x} \left (16-8 x-15 x^2+9 x^3+e^x \left (16+8 x-23 x^2-6 x^3+9 x^4\right )\right )+e^x \left (-16+8 x+15 x^2-9 x^3\right ) \log (1+x)}{16-8 x-15 x^2+9 x^3} \, dx=e^{x+e^x x}-\frac {20}{-4+3 x}-e^x \log (1+x) \]
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Time = 0.72 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.74
method | result | size |
risch | \(-\ln \left (1+x \right ) {\mathrm e}^{x}-\frac {20}{-4+3 x}+{\mathrm e}^{x \left ({\mathrm e}^{x}+1\right )}\) | \(26\) |
parallelrisch | \(\frac {-6 \,{\mathrm e}^{x} \ln \left (1+x \right ) x +6 \,{\mathrm e}^{x \left ({\mathrm e}^{x}+1\right )} x -120+8 \ln \left (1+x \right ) {\mathrm e}^{x}+60 x -8 \,{\mathrm e}^{x \left ({\mathrm e}^{x}+1\right )}}{-8+6 x}\) | \(51\) |
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Time = 0.25 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.06 \[ \int \frac {60+60 x+e^x \left (-16+24 x-9 x^2\right )+e^{x+e^x x} \left (16-8 x-15 x^2+9 x^3+e^x \left (16+8 x-23 x^2-6 x^3+9 x^4\right )\right )+e^x \left (-16+8 x+15 x^2-9 x^3\right ) \log (1+x)}{16-8 x-15 x^2+9 x^3} \, dx=-\frac {{\left (3 \, x - 4\right )} e^{x} \log \left (x + 1\right ) - {\left (3 \, x - 4\right )} e^{\left (x e^{x} + x\right )} + 20}{3 \, x - 4} \]
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Time = 0.25 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.63 \[ \int \frac {60+60 x+e^x \left (-16+24 x-9 x^2\right )+e^{x+e^x x} \left (16-8 x-15 x^2+9 x^3+e^x \left (16+8 x-23 x^2-6 x^3+9 x^4\right )\right )+e^x \left (-16+8 x+15 x^2-9 x^3\right ) \log (1+x)}{16-8 x-15 x^2+9 x^3} \, dx=- e^{x} \log {\left (x + 1 \right )} + e^{x e^{x} + x} - \frac {60}{9 x - 12} \]
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Time = 0.24 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.71 \[ \int \frac {60+60 x+e^x \left (-16+24 x-9 x^2\right )+e^{x+e^x x} \left (16-8 x-15 x^2+9 x^3+e^x \left (16+8 x-23 x^2-6 x^3+9 x^4\right )\right )+e^x \left (-16+8 x+15 x^2-9 x^3\right ) \log (1+x)}{16-8 x-15 x^2+9 x^3} \, dx=-e^{x} \log \left (x + 1\right ) - \frac {20}{3 \, x - 4} + e^{\left (x e^{x} + x\right )} \]
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\[ \int \frac {60+60 x+e^x \left (-16+24 x-9 x^2\right )+e^{x+e^x x} \left (16-8 x-15 x^2+9 x^3+e^x \left (16+8 x-23 x^2-6 x^3+9 x^4\right )\right )+e^x \left (-16+8 x+15 x^2-9 x^3\right ) \log (1+x)}{16-8 x-15 x^2+9 x^3} \, dx=\int { -\frac {{\left (9 \, x^{3} - 15 \, x^{2} - 8 \, x + 16\right )} e^{x} \log \left (x + 1\right ) - {\left (9 \, x^{3} - 15 \, x^{2} + {\left (9 \, x^{4} - 6 \, x^{3} - 23 \, x^{2} + 8 \, x + 16\right )} e^{x} - 8 \, x + 16\right )} e^{\left (x e^{x} + x\right )} + {\left (9 \, x^{2} - 24 \, x + 16\right )} e^{x} - 60 \, x - 60}{9 \, x^{3} - 15 \, x^{2} - 8 \, x + 16} \,d x } \]
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Time = 9.62 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.74 \[ \int \frac {60+60 x+e^x \left (-16+24 x-9 x^2\right )+e^{x+e^x x} \left (16-8 x-15 x^2+9 x^3+e^x \left (16+8 x-23 x^2-6 x^3+9 x^4\right )\right )+e^x \left (-16+8 x+15 x^2-9 x^3\right ) \log (1+x)}{16-8 x-15 x^2+9 x^3} \, dx={\mathrm {e}}^{x\,{\mathrm {e}}^x}\,{\mathrm {e}}^x-\frac {20}{3\,\left (x-\frac {4}{3}\right )}-\ln \left (x+1\right )\,{\mathrm {e}}^x \]
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