Integrand size = 64, antiderivative size = 23 \[ \int \left (e^3 \left (5+e^2\right )+e^{32+2 x} \left (-5+e^2 (-1-2 x)-8 x\right )+9 x+2 e^2 x+\left (e^3+e^{32+2 x} (-1-2 x)+2 x\right ) \log (x)\right ) \, dx=x \left (e^3-e^{2 (16+x)}+x\right ) \left (4+e^2+\log (x)\right ) \]
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Leaf count is larger than twice the leaf count of optimal. \(133\) vs. \(2(23)=46\).
Time = 0.06 (sec) , antiderivative size = 133, normalized size of antiderivative = 5.78, number of steps used = 8, number of rules used = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.078, Rules used = {6, 2218, 2207, 2225, 2634} \[ \int \left (e^3 \left (5+e^2\right )+e^{32+2 x} \left (-5+e^2 (-1-2 x)-8 x\right )+9 x+2 e^2 x+\left (e^3+e^{32+2 x} (-1-2 x)+2 x\right ) \log (x)\right ) \, dx=\frac {1}{2} \left (9+2 e^2\right ) x^2-\frac {x^2}{2}+x^2 \log (x)+e^3 \left (5+e^2\right ) x-e^3 x+\frac {1}{2} e^{2 x+32}-\frac {1}{2} e^{2 x+32} \left (2 \left (4+e^2\right ) x+e^2+5\right )+\frac {1}{2} \left (4+e^2\right ) e^{2 x+32}+e^3 x \log (x)+\frac {1}{2} e^{2 x+32} \log (x)-\frac {1}{2} e^{2 x+32} (2 x+1) \log (x) \]
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Rule 6
Rule 2207
Rule 2218
Rule 2225
Rule 2634
Rubi steps \begin{align*} \text {integral}& = \int \left (e^3 \left (5+e^2\right )+e^{32+2 x} \left (-5+e^2 (-1-2 x)-8 x\right )+\left (9+2 e^2\right ) x+\left (e^3+e^{32+2 x} (-1-2 x)+2 x\right ) \log (x)\right ) \, dx \\ & = e^3 \left (5+e^2\right ) x+\frac {1}{2} \left (9+2 e^2\right ) x^2+\int e^{32+2 x} \left (-5+e^2 (-1-2 x)-8 x\right ) \, dx+\int \left (e^3+e^{32+2 x} (-1-2 x)+2 x\right ) \log (x) \, dx \\ & = e^3 \left (5+e^2\right ) x+\frac {1}{2} \left (9+2 e^2\right ) x^2+\frac {1}{2} e^{32+2 x} \log (x)+e^3 x \log (x)+x^2 \log (x)-\frac {1}{2} e^{32+2 x} (1+2 x) \log (x)-\int \left (e^3-e^{32+2 x}+x\right ) \, dx+\int e^{32+2 x} \left (-5-e^2-2 \left (4+e^2\right ) x\right ) \, dx \\ & = -e^3 x+e^3 \left (5+e^2\right ) x-\frac {x^2}{2}+\frac {1}{2} \left (9+2 e^2\right ) x^2-\frac {1}{2} e^{32+2 x} \left (5+e^2+2 \left (4+e^2\right ) x\right )+\frac {1}{2} e^{32+2 x} \log (x)+e^3 x \log (x)+x^2 \log (x)-\frac {1}{2} e^{32+2 x} (1+2 x) \log (x)-\left (-4-e^2\right ) \int e^{32+2 x} \, dx+\int e^{32+2 x} \, dx \\ & = \frac {1}{2} e^{32+2 x}+\frac {1}{2} e^{32+2 x} \left (4+e^2\right )-e^3 x+e^3 \left (5+e^2\right ) x-\frac {x^2}{2}+\frac {1}{2} \left (9+2 e^2\right ) x^2-\frac {1}{2} e^{32+2 x} \left (5+e^2+2 \left (4+e^2\right ) x\right )+\frac {1}{2} e^{32+2 x} \log (x)+e^3 x \log (x)+x^2 \log (x)-\frac {1}{2} e^{32+2 x} (1+2 x) \log (x) \\ \end{align*}
Time = 0.36 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.13 \[ \int \left (e^3 \left (5+e^2\right )+e^{32+2 x} \left (-5+e^2 (-1-2 x)-8 x\right )+9 x+2 e^2 x+\left (e^3+e^{32+2 x} (-1-2 x)+2 x\right ) \log (x)\right ) \, dx=-\left (\left (-e^3+e^{32+2 x}-x\right ) x \left (4+e^2+\log (x)\right )\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. \(58\) vs. \(2(20)=40\).
Time = 0.09 (sec) , antiderivative size = 59, normalized size of antiderivative = 2.57
method | result | size |
norman | \(x^{2} \ln \left (x \right )+\left (4+{\mathrm e}^{2}\right ) x^{2}+\left (4 \,{\mathrm e}^{3}+{\mathrm e}^{2} {\mathrm e}^{3}\right ) x +x \,{\mathrm e}^{3} \ln \left (x \right )+\left (-{\mathrm e}^{2}-4\right ) x \,{\mathrm e}^{2 x +32}-\ln \left (x \right ) {\mathrm e}^{2 x +32} x\) | \(59\) |
risch | \(x \,{\mathrm e}^{5}+4 x \,{\mathrm e}^{3}-x \,{\mathrm e}^{2 x +34}+x^{2} {\mathrm e}^{2}-\ln \left (x \right ) {\mathrm e}^{2 x +32} x +x \,{\mathrm e}^{3} \ln \left (x \right )+x^{2} \ln \left (x \right )-4 \,{\mathrm e}^{2 x +32} x +4 x^{2}\) | \(63\) |
parts | \(x^{2} \ln \left (x \right )+4 x^{2}+{\mathrm e}^{3} \left (x \ln \left (x \right )-x \right )+\left (-{\mathrm e}^{2}-4\right ) x \,{\mathrm e}^{2 x +32}-\ln \left (x \right ) {\mathrm e}^{2 x +32} x +x \,{\mathrm e}^{2} {\mathrm e}^{3}+x^{2} {\mathrm e}^{2}+5 x \,{\mathrm e}^{3}\) | \(66\) |
parallelrisch | \(x^{2} {\mathrm e}^{2}-{\mathrm e}^{2 x +32} x \,{\mathrm e}^{2}+x \,{\mathrm e}^{3} \ln \left (x \right )+x^{2} \ln \left (x \right )-\ln \left (x \right ) {\mathrm e}^{2 x +32} x -x \,{\mathrm e}^{3}+4 x^{2}-4 \,{\mathrm e}^{2 x +32} x +\left ({\mathrm e}^{2}+5\right ) {\mathrm e}^{3} x\) | \(69\) |
default | \(\left ({\mathrm e}^{2}+5\right ) {\mathrm e}^{3} x -2 \left (2 x +32\right ) {\mathrm e}^{2 x +32}+64 \,{\mathrm e}^{2 x +32}+\frac {31 \,{\mathrm e}^{2} {\mathrm e}^{2 x +32}}{2}-\frac {{\mathrm e}^{2} \left (\left (2 x +32\right ) {\mathrm e}^{2 x +32}-{\mathrm e}^{2 x +32}\right )}{2}+x^{2} \ln \left (x \right )+4 x^{2}+{\mathrm e}^{3} \left (x \ln \left (x \right )-x \right )-\ln \left (x \right ) {\mathrm e}^{2 x +32} x +x^{2} {\mathrm e}^{2}\) | \(105\) |
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Leaf count of result is larger than twice the leaf count of optimal. 57 vs. \(2 (20) = 40\).
Time = 0.25 (sec) , antiderivative size = 57, normalized size of antiderivative = 2.48 \[ \int \left (e^3 \left (5+e^2\right )+e^{32+2 x} \left (-5+e^2 (-1-2 x)-8 x\right )+9 x+2 e^2 x+\left (e^3+e^{32+2 x} (-1-2 x)+2 x\right ) \log (x)\right ) \, dx=x^{2} e^{2} + 4 \, x^{2} + x e^{5} + 4 \, x e^{3} - {\left (x e^{2} + 4 \, x\right )} e^{\left (2 \, x + 32\right )} + {\left (x^{2} + x e^{3} - x e^{\left (2 \, x + 32\right )}\right )} \log \left (x\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. 51 vs. \(2 (20) = 40\).
Time = 0.15 (sec) , antiderivative size = 51, normalized size of antiderivative = 2.22 \[ \int \left (e^3 \left (5+e^2\right )+e^{32+2 x} \left (-5+e^2 (-1-2 x)-8 x\right )+9 x+2 e^2 x+\left (e^3+e^{32+2 x} (-1-2 x)+2 x\right ) \log (x)\right ) \, dx=x^{2} \cdot \left (4 + e^{2}\right ) + x \left (4 e^{3} + e^{5}\right ) + \left (x^{2} + x e^{3}\right ) \log {\left (x \right )} + \left (- x \log {\left (x \right )} - x e^{2} - 4 x\right ) e^{2 x + 32} \]
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Leaf count of result is larger than twice the leaf count of optimal. 72 vs. \(2 (20) = 40\).
Time = 0.19 (sec) , antiderivative size = 72, normalized size of antiderivative = 3.13 \[ \int \left (e^3 \left (5+e^2\right )+e^{32+2 x} \left (-5+e^2 (-1-2 x)-8 x\right )+9 x+2 e^2 x+\left (e^3+e^{32+2 x} (-1-2 x)+2 x\right ) \log (x)\right ) \, dx=x {\left (e^{2} + 5\right )} e^{3} + x^{2} e^{2} + 4 \, x^{2} - x e^{3} - \frac {1}{2} \, {\left (2 \, x {\left (e^{34} + 4 \, e^{32}\right )} + e^{32}\right )} e^{\left (2 \, x\right )} + {\left (x^{2} + x e^{3} - x e^{\left (2 \, x + 32\right )}\right )} \log \left (x\right ) + \frac {1}{2} \, e^{\left (2 \, x + 32\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 75 vs. \(2 (20) = 40\).
Time = 0.28 (sec) , antiderivative size = 75, normalized size of antiderivative = 3.26 \[ \int \left (e^3 \left (5+e^2\right )+e^{32+2 x} \left (-5+e^2 (-1-2 x)-8 x\right )+9 x+2 e^2 x+\left (e^3+e^{32+2 x} (-1-2 x)+2 x\right ) \log (x)\right ) \, dx=x {\left (e^{2} + 5\right )} e^{3} + x^{2} e^{2} + 4 \, x^{2} - x e^{3} - x e^{\left (2 \, x + 34\right )} - \frac {1}{2} \, {\left (8 \, x + 1\right )} e^{\left (2 \, x + 32\right )} + {\left (x^{2} + x e^{3} - x e^{\left (2 \, x + 32\right )}\right )} \log \left (x\right ) + \frac {1}{2} \, e^{\left (2 \, x + 32\right )} \]
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Time = 7.78 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.87 \[ \int \left (e^3 \left (5+e^2\right )+e^{32+2 x} \left (-5+e^2 (-1-2 x)-8 x\right )+9 x+2 e^2 x+\left (e^3+e^{32+2 x} (-1-2 x)+2 x\right ) \log (x)\right ) \, dx=x\,\left (x+{\mathrm {e}}^3-{\mathrm {e}}^{2\,x+32}\right )\,\left ({\mathrm {e}}^2+\ln \left (x\right )+4\right ) \]
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