Optimal. Leaf size=15 \[ \frac {6^{\frac {-1+15 x}{x^4}}}{x} \]
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Rubi [B] time = 0.07, antiderivative size = 39, normalized size of antiderivative = 2.60, number of steps used = 1, number of rules used = 1, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.034, Rules used = {2288} \begin {gather*} \frac {6^{-\frac {1-15 x}{x^4}} (4-45 x)}{\left (\frac {4 (1-15 x)}{x^5}+\frac {15}{x^4}\right ) x^6} \end {gather*}
Antiderivative was successfully verified.
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Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {6^{-\frac {1-15 x}{x^4}} (4-45 x)}{\left (\frac {4 (1-15 x)}{x^5}+\frac {15}{x^4}\right ) x^6}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 15, normalized size = 1.00 \begin {gather*} \frac {6^{\frac {-1+15 x}{x^4}}}{x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.26, size = 15, normalized size = 1.00 \begin {gather*} \frac {6^{\frac {15 \, x - 1}{x^{4}}}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -\frac {{\left (x^{4} + {\left (45 \, x - 4\right )} \log \relax (6)\right )} 6^{\frac {15 \, x - 1}{x^{4}}}}{x^{6}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.12, size = 17, normalized size = 1.13
method | result | size |
gosper | \(\frac {{\mathrm e}^{\frac {\left (15 x -1\right ) \ln \relax (6)}{x^{4}}}}{x}\) | \(17\) |
norman | \(\frac {{\mathrm e}^{\frac {\left (15 x -1\right ) \ln \relax (6)}{x^{4}}}}{x}\) | \(17\) |
risch | \(\frac {{\mathrm e}^{\frac {\left (15 x -1\right ) \left (\ln \relax (2)+\ln \relax (3)\right )}{x^{4}}}}{x}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.50, size = 34, normalized size = 2.27 \begin {gather*} \frac {e^{\left (\frac {15 \, \log \relax (3)}{x^{3}} + \frac {15 \, \log \relax (2)}{x^{3}} - \frac {\log \relax (3)}{x^{4}} - \frac {\log \relax (2)}{x^{4}}\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 6.73, size = 15, normalized size = 1.00 \begin {gather*} \frac {6^{\frac {15\,x-1}{x^4}}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.20, size = 14, normalized size = 0.93 \begin {gather*} \frac {e^{\frac {\left (15 x - 1\right ) \log {\relax (6 )}}{x^{4}}}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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