Optimal. Leaf size=18 \[ e^{-\frac {75}{x \left (x+x^4-\log (2)\right )}} \]
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Rubi [A]
time = 0.82, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 3, integrand size = 73, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.041, Rules used = {6820, 12, 6838}
\begin {gather*} e^{-\frac {75}{x \left (x^4+x-\log (2)\right )}} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6820
Rule 6838
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {75 e^{-\frac {75}{x \left (x+x^4-\log (2)\right )}} \left (2 x+5 x^4-\log (2)\right )}{x^2 \left (x+x^4-\log (2)\right )^2} \, dx\\ &=75 \int \frac {e^{-\frac {75}{x \left (x+x^4-\log (2)\right )}} \left (2 x+5 x^4-\log (2)\right )}{x^2 \left (x+x^4-\log (2)\right )^2} \, dx\\ &=e^{-\frac {75}{x \left (x+x^4-\log (2)\right )}}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.14, size = 18, normalized size = 1.00 \begin {gather*} e^{-\frac {75}{x^2+x^5-x \log (2)}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.37, size = 20, normalized size = 1.11
method | result | size |
gosper | \({\mathrm e}^{\frac {75}{x \left (-x^{4}+\ln \left (2\right )-x \right )}}\) | \(20\) |
risch | \({\mathrm e}^{\frac {75}{x \left (-x^{4}+\ln \left (2\right )-x \right )}}\) | \(20\) |
norman | \(\frac {x \ln \left (2\right ) {\mathrm e}^{-\frac {75}{x^{5}-x \ln \left (2\right )+x^{2}}}-x^{2} {\mathrm e}^{-\frac {75}{x^{5}-x \ln \left (2\right )+x^{2}}}-x^{5} {\mathrm e}^{-\frac {75}{x^{5}-x \ln \left (2\right )+x^{2}}}}{x \left (-x^{4}+\ln \left (2\right )-x \right )}\) | \(84\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 56 vs.
\(2 (17) = 34\).
time = 0.59, size = 56, normalized size = 3.11 \begin {gather*} e^{\left (-\frac {75 \, x^{3}}{x^{4} \log \left (2\right ) + x \log \left (2\right ) - \log \left (2\right )^{2}} - \frac {75}{x^{4} \log \left (2\right ) + x \log \left (2\right ) - \log \left (2\right )^{2}} + \frac {75}{x \log \left (2\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 17, normalized size = 0.94 \begin {gather*} e^{\left (-\frac {75}{x^{5} + x^{2} - x \log \left (2\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.45, size = 15, normalized size = 0.83 \begin {gather*} e^{- \frac {75}{x^{5} + x^{2} - x \log {\left (2 \right )}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 17, normalized size = 0.94 \begin {gather*} e^{\left (-\frac {75}{x^{5} + x^{2} - x \log \left (2\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.56, size = 17, normalized size = 0.94 \begin {gather*} {\mathrm {e}}^{-\frac {75}{x^5+x^2-\ln \left (2\right )\,x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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