Integrand size = 34, antiderivative size = 25 \[ \int e^{\frac {2 \left (2+\left (450 x+525 x^2\right ) \log (4)\right )}{x}} \left (-4+2 x+1050 x^2 \log (4)\right ) \, dx=e^{\frac {2 (2+75 x (x+6 (1+x)) \log (4))}{x}} x^2 \]
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Leaf count is larger than twice the leaf count of optimal. \(69\) vs. \(2(25)=50\).
Time = 0.04 (sec) , antiderivative size = 69, normalized size of antiderivative = 2.76, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.029, Rules used = {2326} \[ \int e^{\frac {2 \left (2+\left (450 x+525 x^2\right ) \log (4)\right )}{x}} \left (-4+2 x+1050 x^2 \log (4)\right ) \, dx=-\frac {4^{\frac {2 \left (525 x^2+450 x\right )}{x}} e^{4/x} \left (2-525 x^2 \log (4)\right )}{\frac {150 (7 x+3) \log (4)}{x}-\frac {75 \left (7 x^2+6 x\right ) \log (4)+2}{x^2}} \]
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Rule 2326
Rubi steps \begin{align*} \text {integral}& = -\frac {4^{\frac {2 \left (450 x+525 x^2\right )}{x}} e^{4/x} \left (2-525 x^2 \log (4)\right )}{\frac {150 (3+7 x) \log (4)}{x}-\frac {2+75 \left (6 x+7 x^2\right ) \log (4)}{x^2}} \\ \end{align*}
Time = 0.03 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.72 \[ \int e^{\frac {2 \left (2+\left (450 x+525 x^2\right ) \log (4)\right )}{x}} \left (-4+2 x+1050 x^2 \log (4)\right ) \, dx=2^{1800+2100 x} e^{4/x} x^2 \]
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Time = 0.54 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.00
method | result | size |
risch | \(x^{2} {\mathrm e}^{\frac {2100 x^{2} \ln \left (2\right )+1800 x \ln \left (2\right )+4}{x}}\) | \(25\) |
gosper | \(x^{2} {\mathrm e}^{\frac {2100 x^{2} \ln \left (2\right )+1800 x \ln \left (2\right )+4}{x}}\) | \(27\) |
norman | \(x^{2} {\mathrm e}^{\frac {4 \left (525 x^{2}+450 x \right ) \ln \left (2\right )+4}{x}}\) | \(27\) |
parallelrisch | \(x^{2} {\mathrm e}^{\frac {4 \left (525 x^{2}+450 x \right ) \ln \left (2\right )+4}{x}}\) | \(27\) |
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Time = 0.24 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.00 \[ \int e^{\frac {2 \left (2+\left (450 x+525 x^2\right ) \log (4)\right )}{x}} \left (-4+2 x+1050 x^2 \log (4)\right ) \, dx=x^{2} e^{\left (\frac {4 \, {\left (75 \, {\left (7 \, x^{2} + 6 \, x\right )} \log \left (2\right ) + 1\right )}}{x}\right )} \]
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Time = 0.09 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.80 \[ \int e^{\frac {2 \left (2+\left (450 x+525 x^2\right ) \log (4)\right )}{x}} \left (-4+2 x+1050 x^2 \log (4)\right ) \, dx=x^{2} e^{\frac {2 \left (\left (1050 x^{2} + 900 x\right ) \log {\left (2 \right )} + 2\right )}{x}} \]
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Time = 0.31 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.68 \[ \int e^{\frac {2 \left (2+\left (450 x+525 x^2\right ) \log (4)\right )}{x}} \left (-4+2 x+1050 x^2 \log (4)\right ) \, dx=71448348576730208360402604523024658663907311448489024669693316988935593287322878666163481950176220037593478347105937422686501991894419788796088422137966026262523598150372719976137911322484446114613284904383977643176193557817897027023063420124852033989626806764509137929914787205373413116077254242653423277386226627159120168223623660139965116969572411841665962582988716865792650075294655252525257343163566042824495509307872827973214736884381496689456792434150079470111661811761376161068055664012337698456291039551943299284254570579952324837376 \, x^{2} e^{\left (2100 \, x \log \left (2\right ) + \frac {4}{x}\right )} \]
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Time = 0.29 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.96 \[ \int e^{\frac {2 \left (2+\left (450 x+525 x^2\right ) \log (4)\right )}{x}} \left (-4+2 x+1050 x^2 \log (4)\right ) \, dx=x^{2} e^{\left (\frac {4 \, {\left (525 \, x^{2} \log \left (2\right ) + 450 \, x \log \left (2\right ) + 1\right )}}{x}\right )} \]
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Time = 12.28 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.68 \[ \int e^{\frac {2 \left (2+\left (450 x+525 x^2\right ) \log (4)\right )}{x}} \left (-4+2 x+1050 x^2 \log (4)\right ) \, dx=2^{2100\,x+1800}\,x^2\,{\mathrm {e}}^{4/x} \]
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