Integrand size = 61, antiderivative size = 26 \[ \int \frac {25+9 x^3-21 x^4+e^{2 x} \left (x^2-2 x^3-2 x^4\right )+\left (-25+14 x^3+e^{2 x} \left (x^2+2 x^3\right )\right ) \log (x)}{x^2} \, dx=x \left (x-\left (e^{2 x}+\frac {25}{x^2}+7 x\right ) (x-\log (x))\right ) \]
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Time = 0.06 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.50, number of steps used = 9, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.049, Rules used = {14, 2326, 2372} \[ \int \frac {25+9 x^3-21 x^4+e^{2 x} \left (x^2-2 x^3-2 x^4\right )+\left (-25+14 x^3+e^{2 x} \left (x^2+2 x^3\right )\right ) \log (x)}{x^2} \, dx=-7 x^3+x^2+7 x^2 \log (x)-e^{2 x} \left (x^2-x \log (x)\right )+\frac {25 \log (x)}{x} \]
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Rule 14
Rule 2326
Rule 2372
Rubi steps \begin{align*} \text {integral}& = \int \left (-e^{2 x} \left (-1+2 x+2 x^2-\log (x)-2 x \log (x)\right )+\frac {25+9 x^3-21 x^4-25 \log (x)+14 x^3 \log (x)}{x^2}\right ) \, dx \\ & = -\int e^{2 x} \left (-1+2 x+2 x^2-\log (x)-2 x \log (x)\right ) \, dx+\int \frac {25+9 x^3-21 x^4-25 \log (x)+14 x^3 \log (x)}{x^2} \, dx \\ & = -e^{2 x} \left (x^2-x \log (x)\right )+\int \left (\frac {25+9 x^3-21 x^4}{x^2}+\frac {\left (-25+14 x^3\right ) \log (x)}{x^2}\right ) \, dx \\ & = -e^{2 x} \left (x^2-x \log (x)\right )+\int \frac {25+9 x^3-21 x^4}{x^2} \, dx+\int \frac {\left (-25+14 x^3\right ) \log (x)}{x^2} \, dx \\ & = \frac {25 \log (x)}{x}+7 x^2 \log (x)-e^{2 x} \left (x^2-x \log (x)\right )-\int \left (\frac {25}{x^2}+7 x\right ) \, dx+\int \left (\frac {25}{x^2}+9 x-21 x^2\right ) \, dx \\ & = x^2-7 x^3+\frac {25 \log (x)}{x}+7 x^2 \log (x)-e^{2 x} \left (x^2-x \log (x)\right ) \\ \end{align*}
Time = 0.22 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.42 \[ \int \frac {25+9 x^3-21 x^4+e^{2 x} \left (x^2-2 x^3-2 x^4\right )+\left (-25+14 x^3+e^{2 x} \left (x^2+2 x^3\right )\right ) \log (x)}{x^2} \, dx=-x^2 \left (-1+e^{2 x}+7 x\right )+\left (\frac {25}{x}+e^{2 x} x+7 x^2\right ) \log (x) \]
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Time = 0.11 (sec) , antiderivative size = 40, normalized size of antiderivative = 1.54
method | result | size |
risch | \(\frac {\left ({\mathrm e}^{2 x} x^{2}+7 x^{3}+25\right ) \ln \left (x \right )}{x}-{\mathrm e}^{2 x} x^{2}-7 x^{3}+x^{2}\) | \(40\) |
default | \(x \,{\mathrm e}^{2 x} \ln \left (x \right )-{\mathrm e}^{2 x} x^{2}+7 x^{2} \ln \left (x \right )+x^{2}+\frac {25 \ln \left (x \right )}{x}-7 x^{3}\) | \(41\) |
parts | \(x \,{\mathrm e}^{2 x} \ln \left (x \right )-{\mathrm e}^{2 x} x^{2}+7 x^{2} \ln \left (x \right )+x^{2}+\frac {25 \ln \left (x \right )}{x}-7 x^{3}\) | \(41\) |
parallelrisch | \(\frac {{\mathrm e}^{2 x} \ln \left (x \right ) x^{2}-{\mathrm e}^{2 x} x^{3}+7 x^{3} \ln \left (x \right )-7 x^{4}+x^{3}+25 \ln \left (x \right )}{x}\) | \(44\) |
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Time = 0.26 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.65 \[ \int \frac {25+9 x^3-21 x^4+e^{2 x} \left (x^2-2 x^3-2 x^4\right )+\left (-25+14 x^3+e^{2 x} \left (x^2+2 x^3\right )\right ) \log (x)}{x^2} \, dx=-\frac {7 \, x^{4} + x^{3} e^{\left (2 \, x\right )} - x^{3} - {\left (7 \, x^{3} + x^{2} e^{\left (2 \, x\right )} + 25\right )} \log \left (x\right )}{x} \]
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Time = 0.12 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.23 \[ \int \frac {25+9 x^3-21 x^4+e^{2 x} \left (x^2-2 x^3-2 x^4\right )+\left (-25+14 x^3+e^{2 x} \left (x^2+2 x^3\right )\right ) \log (x)}{x^2} \, dx=- 7 x^{3} + x^{2} + \left (- x^{2} + x \log {\left (x \right )}\right ) e^{2 x} + \frac {\left (7 x^{3} + 25\right ) \log {\left (x \right )}}{x} \]
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\[ \int \frac {25+9 x^3-21 x^4+e^{2 x} \left (x^2-2 x^3-2 x^4\right )+\left (-25+14 x^3+e^{2 x} \left (x^2+2 x^3\right )\right ) \log (x)}{x^2} \, dx=\int { -\frac {21 \, x^{4} - 9 \, x^{3} + {\left (2 \, x^{4} + 2 \, x^{3} - x^{2}\right )} e^{\left (2 \, x\right )} - {\left (14 \, x^{3} + {\left (2 \, x^{3} + x^{2}\right )} e^{\left (2 \, x\right )} - 25\right )} \log \left (x\right ) - 25}{x^{2}} \,d x } \]
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Time = 0.26 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.77 \[ \int \frac {25+9 x^3-21 x^4+e^{2 x} \left (x^2-2 x^3-2 x^4\right )+\left (-25+14 x^3+e^{2 x} \left (x^2+2 x^3\right )\right ) \log (x)}{x^2} \, dx=-\frac {7 \, x^{4} + x^{3} e^{\left (2 \, x\right )} - 7 \, x^{3} \log \left (x\right ) - x^{2} e^{\left (2 \, x\right )} \log \left (x\right ) - x^{3} - 25 \, \log \left (x\right )}{x} \]
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Time = 14.34 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.42 \[ \int \frac {25+9 x^3-21 x^4+e^{2 x} \left (x^2-2 x^3-2 x^4\right )+\left (-25+14 x^3+e^{2 x} \left (x^2+2 x^3\right )\right ) \log (x)}{x^2} \, dx=\frac {25\,\ln \left (x\right )}{x}+x^2\,\left (7\,\ln \left (x\right )-{\mathrm {e}}^{2\,x}+1\right )-7\,x^3+x\,{\mathrm {e}}^{2\,x}\,\ln \left (x\right ) \]
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