Integrand size = 27, antiderivative size = 23 \[ \int \left (-e^{21}+e^{4+x} (-15-15 x)+60 x-e^{21} \log (x)\right ) \, dx=x \left (15 \left (-e^{4+x}+2 x\right )-e^{21} \log (x)\right ) \]
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Time = 0.01 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.35, number of steps used = 4, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {2207, 2225, 2332} \[ \int \left (-e^{21}+e^{4+x} (-15-15 x)+60 x-e^{21} \log (x)\right ) \, dx=30 x^2+15 e^{x+4}-15 e^{x+4} (x+1)-e^{21} x \log (x) \]
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Rule 2207
Rule 2225
Rule 2332
Rubi steps \begin{align*} \text {integral}& = -e^{21} x+30 x^2-e^{21} \int \log (x) \, dx+\int e^{4+x} (-15-15 x) \, dx \\ & = 30 x^2-15 e^{4+x} (1+x)-e^{21} x \log (x)+15 \int e^{4+x} \, dx \\ & = 15 e^{4+x}+30 x^2-15 e^{4+x} (1+x)-e^{21} x \log (x) \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.96 \[ \int \left (-e^{21}+e^{4+x} (-15-15 x)+60 x-e^{21} \log (x)\right ) \, dx=-15 e^{4+x} x+30 x^2-e^{21} x \log (x) \]
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Time = 0.04 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.91
method | result | size |
norman | \(30 x^{2}-15 x \,{\mathrm e}^{4+x}-x \,{\mathrm e}^{21} \ln \left (x \right )\) | \(21\) |
risch | \(30 x^{2}-15 x \,{\mathrm e}^{4+x}-x \,{\mathrm e}^{21} \ln \left (x \right )\) | \(21\) |
parallelrisch | \(30 x^{2}-15 x \,{\mathrm e}^{4+x}-x \,{\mathrm e}^{21} \ln \left (x \right )\) | \(21\) |
default | \(-15 \,{\mathrm e}^{4+x} \left (4+x \right )+60 \,{\mathrm e}^{4+x}+30 x^{2}-{\mathrm e}^{21} \left (x \ln \left (x \right )-x \right )-x \,{\mathrm e}^{21}\) | \(39\) |
parts | \(-15 \,{\mathrm e}^{4+x} \left (4+x \right )+60 \,{\mathrm e}^{4+x}+30 x^{2}-{\mathrm e}^{21} \left (x \ln \left (x \right )-x \right )-x \,{\mathrm e}^{21}\) | \(39\) |
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Time = 0.24 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.87 \[ \int \left (-e^{21}+e^{4+x} (-15-15 x)+60 x-e^{21} \log (x)\right ) \, dx=-x e^{21} \log \left (x\right ) + 30 \, x^{2} - 15 \, x e^{\left (x + 4\right )} \]
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Time = 0.09 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.87 \[ \int \left (-e^{21}+e^{4+x} (-15-15 x)+60 x-e^{21} \log (x)\right ) \, dx=30 x^{2} - 15 x e^{x + 4} - x e^{21} \log {\left (x \right )} \]
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none
Time = 0.19 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.30 \[ \int \left (-e^{21}+e^{4+x} (-15-15 x)+60 x-e^{21} \log (x)\right ) \, dx=30 \, x^{2} - {\left (x \log \left (x\right ) - x\right )} e^{21} - x e^{21} - 15 \, x e^{\left (x + 4\right )} \]
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Time = 0.26 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.30 \[ \int \left (-e^{21}+e^{4+x} (-15-15 x)+60 x-e^{21} \log (x)\right ) \, dx=30 \, x^{2} - {\left (x \log \left (x\right ) - x\right )} e^{21} - x e^{21} - 15 \, x e^{\left (x + 4\right )} \]
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Time = 16.43 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.78 \[ \int \left (-e^{21}+e^{4+x} (-15-15 x)+60 x-e^{21} \log (x)\right ) \, dx=-x\,\left (15\,{\mathrm {e}}^{x+4}-30\,x+{\mathrm {e}}^{21}\,\ln \left (x\right )\right ) \]
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