Integrand size = 36, antiderivative size = 21 \[ \int \frac {-x-25 e^x x+2 x^2+10 e^x \log (x)+5 e^x x \log ^2(x)}{x} \, dx=13-x+x^2-5 e^x \left (5-\log ^2(x)\right ) \]
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Time = 0.03 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.24, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {14, 2326} \[ \int \frac {-x-25 e^x x+2 x^2+10 e^x \log (x)+5 e^x x \log ^2(x)}{x} \, dx=x^2-x-\frac {5 e^x \left (5 x-x \log ^2(x)\right )}{x} \]
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Rule 14
Rule 2326
Rubi steps \begin{align*} \text {integral}& = \int \left (-1+2 x+\frac {5 e^x \left (-5 x+2 \log (x)+x \log ^2(x)\right )}{x}\right ) \, dx \\ & = -x+x^2+5 \int \frac {e^x \left (-5 x+2 \log (x)+x \log ^2(x)\right )}{x} \, dx \\ & = -x+x^2-\frac {5 e^x \left (5 x-x \log ^2(x)\right )}{x} \\ \end{align*}
Time = 0.07 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.95 \[ \int \frac {-x-25 e^x x+2 x^2+10 e^x \log (x)+5 e^x x \log ^2(x)}{x} \, dx=-25 e^x+(-1+x) x+5 e^x \log ^2(x) \]
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Time = 0.88 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.95
method | result | size |
default | \(-x +5 \,{\mathrm e}^{x} \ln \left (x \right )^{2}-25 \,{\mathrm e}^{x}+x^{2}\) | \(20\) |
norman | \(-x +5 \,{\mathrm e}^{x} \ln \left (x \right )^{2}-25 \,{\mathrm e}^{x}+x^{2}\) | \(20\) |
risch | \(-x +5 \,{\mathrm e}^{x} \ln \left (x \right )^{2}-25 \,{\mathrm e}^{x}+x^{2}\) | \(20\) |
parallelrisch | \(-x +5 \,{\mathrm e}^{x} \ln \left (x \right )^{2}-25 \,{\mathrm e}^{x}+x^{2}\) | \(20\) |
parts | \(-x +5 \,{\mathrm e}^{x} \ln \left (x \right )^{2}-25 \,{\mathrm e}^{x}+x^{2}\) | \(20\) |
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Time = 0.25 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.90 \[ \int \frac {-x-25 e^x x+2 x^2+10 e^x \log (x)+5 e^x x \log ^2(x)}{x} \, dx=5 \, e^{x} \log \left (x\right )^{2} + x^{2} - x - 25 \, e^{x} \]
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Time = 0.11 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.71 \[ \int \frac {-x-25 e^x x+2 x^2+10 e^x \log (x)+5 e^x x \log ^2(x)}{x} \, dx=x^{2} - x + \left (5 \log {\left (x \right )}^{2} - 25\right ) e^{x} \]
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Time = 0.24 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.90 \[ \int \frac {-x-25 e^x x+2 x^2+10 e^x \log (x)+5 e^x x \log ^2(x)}{x} \, dx=5 \, e^{x} \log \left (x\right )^{2} + x^{2} - x - 25 \, e^{x} \]
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Time = 0.26 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.90 \[ \int \frac {-x-25 e^x x+2 x^2+10 e^x \log (x)+5 e^x x \log ^2(x)}{x} \, dx=5 \, e^{x} \log \left (x\right )^{2} + x^{2} - x - 25 \, e^{x} \]
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Time = 9.03 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.90 \[ \int \frac {-x-25 e^x x+2 x^2+10 e^x \log (x)+5 e^x x \log ^2(x)}{x} \, dx=5\,{\mathrm {e}}^x\,{\ln \left (x\right )}^2-25\,{\mathrm {e}}^x-x+x^2 \]
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