Integrand size = 60, antiderivative size = 19 \[ \int \frac {-4 x^2+e^{\frac {25+1250 x+15675 x^2+1250 x^3+25 x^4}{x^2}} \left (-50-1250 x+1250 x^3+50 x^4\right ) \log ^2(x)}{x^3 \log ^2(x)} \, dx=e^{25 \left (25+\frac {1}{x}+x\right )^2}+\frac {4}{\log (x)} \]
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Time = 0.59 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.26, number of steps used = 6, number of rules used = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {6820, 14, 6838, 2339, 30} \[ \int \frac {-4 x^2+e^{\frac {25+1250 x+15675 x^2+1250 x^3+25 x^4}{x^2}} \left (-50-1250 x+1250 x^3+50 x^4\right ) \log ^2(x)}{x^3 \log ^2(x)} \, dx=e^{\frac {25 \left (x^2+25 x+1\right )^2}{x^2}}+\frac {4}{\log (x)} \]
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Rule 14
Rule 30
Rule 2339
Rule 6820
Rule 6838
Rubi steps \begin{align*} \text {integral}& = \int \frac {50 e^{\frac {25 \left (1+25 x+x^2\right )^2}{x^2}} \left (-1-25 x+25 x^3+x^4\right )-\frac {4 x^2}{\log ^2(x)}}{x^3} \, dx \\ & = \int \left (\frac {50 e^{\frac {25 \left (1+25 x+x^2\right )^2}{x^2}} (-1+x) (1+x) \left (1+25 x+x^2\right )}{x^3}-\frac {4}{x \log ^2(x)}\right ) \, dx \\ & = -\left (4 \int \frac {1}{x \log ^2(x)} \, dx\right )+50 \int \frac {e^{\frac {25 \left (1+25 x+x^2\right )^2}{x^2}} (-1+x) (1+x) \left (1+25 x+x^2\right )}{x^3} \, dx \\ & = e^{\frac {25 \left (1+25 x+x^2\right )^2}{x^2}}-4 \text {Subst}\left (\int \frac {1}{x^2} \, dx,x,\log (x)\right ) \\ & = e^{\frac {25 \left (1+25 x+x^2\right )^2}{x^2}}+\frac {4}{\log (x)} \\ \end{align*}
Time = 0.42 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.26 \[ \int \frac {-4 x^2+e^{\frac {25+1250 x+15675 x^2+1250 x^3+25 x^4}{x^2}} \left (-50-1250 x+1250 x^3+50 x^4\right ) \log ^2(x)}{x^3 \log ^2(x)} \, dx=e^{\frac {25 \left (1+25 x+x^2\right )^2}{x^2}}+\frac {4}{\log (x)} \]
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Time = 0.14 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.26
method | result | size |
risch | \(\frac {4}{\ln \left (x \right )}+{\mathrm e}^{\frac {25 \left (x^{2}+25 x +1\right )^{2}}{x^{2}}}\) | \(24\) |
default | \(\frac {4}{\ln \left (x \right )}+{\mathrm e}^{\frac {25 x^{4}+1250 x^{3}+15675 x^{2}+1250 x +25}{x^{2}}}\) | \(33\) |
parts | \(\frac {4}{\ln \left (x \right )}+{\mathrm e}^{\frac {25 x^{4}+1250 x^{3}+15675 x^{2}+1250 x +25}{x^{2}}}\) | \(33\) |
parallelrisch | \(-\frac {-{\mathrm e}^{\frac {25 x^{4}+1250 x^{3}+15675 x^{2}+1250 x +25}{x^{2}}} \ln \left (x \right )-4}{\ln \left (x \right )}\) | \(37\) |
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Time = 0.25 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.79 \[ \int \frac {-4 x^2+e^{\frac {25+1250 x+15675 x^2+1250 x^3+25 x^4}{x^2}} \left (-50-1250 x+1250 x^3+50 x^4\right ) \log ^2(x)}{x^3 \log ^2(x)} \, dx=\frac {e^{\left (\frac {25 \, {\left (x^{4} + 50 \, x^{3} + 627 \, x^{2} + 50 \, x + 1\right )}}{x^{2}}\right )} \log \left (x\right ) + 4}{\log \left (x\right )} \]
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Time = 0.15 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.53 \[ \int \frac {-4 x^2+e^{\frac {25+1250 x+15675 x^2+1250 x^3+25 x^4}{x^2}} \left (-50-1250 x+1250 x^3+50 x^4\right ) \log ^2(x)}{x^3 \log ^2(x)} \, dx=e^{\frac {25 x^{4} + 1250 x^{3} + 15675 x^{2} + 1250 x + 25}{x^{2}}} + \frac {4}{\log {\left (x \right )}} \]
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Time = 0.34 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.63 \[ \int \frac {-4 x^2+e^{\frac {25+1250 x+15675 x^2+1250 x^3+25 x^4}{x^2}} \left (-50-1250 x+1250 x^3+50 x^4\right ) \log ^2(x)}{x^3 \log ^2(x)} \, dx=\frac {e^{\left (25 \, x^{2} + 1250 \, x + \frac {1250}{x} + \frac {25}{x^{2}} + 15675\right )} \log \left (x\right ) + 4}{\log \left (x\right )} \]
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Time = 0.27 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.79 \[ \int \frac {-4 x^2+e^{\frac {25+1250 x+15675 x^2+1250 x^3+25 x^4}{x^2}} \left (-50-1250 x+1250 x^3+50 x^4\right ) \log ^2(x)}{x^3 \log ^2(x)} \, dx=\frac {e^{\left (\frac {25 \, {\left (x^{4} + 50 \, x^{3} + 627 \, x^{2} + 50 \, x + 1\right )}}{x^{2}}\right )} \log \left (x\right ) + 4}{\log \left (x\right )} \]
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Time = 12.13 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.68 \[ \int \frac {-4 x^2+e^{\frac {25+1250 x+15675 x^2+1250 x^3+25 x^4}{x^2}} \left (-50-1250 x+1250 x^3+50 x^4\right ) \log ^2(x)}{x^3 \log ^2(x)} \, dx=\frac {4}{\ln \left (x\right )}+{\mathrm {e}}^{1250\,x}\,{\mathrm {e}}^{15675}\,{\mathrm {e}}^{\frac {25}{x^2}}\,{\mathrm {e}}^{25\,x^2}\,{\mathrm {e}}^{1250/x} \]
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