Optimal. Leaf size=15 \[ \frac {6^{\frac {-1+15 x}{x^4}}}{x} \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(39\) vs. \(2(15)=30\).
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 = {2326}
\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 2326
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 = 0.03, 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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Maple [A]
time = 1.66, size = 17, normalized size = 1.13
method | result | size |
gosper | \(\frac {{\mathrm e}^{\frac {\left (15 x -1\right ) \ln \left (6\right )}{x^{4}}}}{x}\) | \(17\) |
norman | \(\frac {{\mathrm e}^{\frac {\left (15 x -1\right ) \ln \left (6\right )}{x^{4}}}}{x}\) | \(17\) |
risch | \(\frac {{\mathrm e}^{\frac {\left (15 x -1\right ) \left (\ln \left (2\right )+\ln \left (3\right )\right )}{x^{4}}}}{x}\) | \(20\) |
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. 34 vs.
\(2 (15) = 30\).
time = 0.53, size = 34, normalized size = 2.27 \begin {gather*} \frac {e^{\left (\frac {15 \, \log \left (3\right )}{x^{3}} + \frac {15 \, \log \left (2\right )}{x^{3}} - \frac {\log \left (3\right )}{x^{4}} - \frac {\log \left (2\right )}{x^{4}}\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, 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 = 0.06, size = 14, normalized size = 0.93 \begin {gather*} \frac {e^{\frac {\left (15 x - 1\right ) \log {\left (6 \right )}}{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*} \text {could not integrate} \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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