Optimal. Leaf size=16 \[ \frac {2 e^{4 x}}{3 x^2 \log (x)} \]
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Rubi [A]
time = 0.28, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps
used = 4, number of rules used = 3, integrand size = 32, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.094, Rules used = {12, 6873, 2326}
\begin {gather*} \frac {2 e^{4 x}}{3 x^2 \log (x)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2326
Rule 6873
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{3} \int \frac {-2 e^{4 x}+e^{4 x} (-4+8 x) \log (x)}{x^3 \log ^2(x)} \, dx\\ &=\frac {1}{3} \int \frac {2 e^{4 x} (-1-2 \log (x)+4 x \log (x))}{x^3 \log ^2(x)} \, dx\\ &=\frac {2}{3} \int \frac {e^{4 x} (-1-2 \log (x)+4 x \log (x))}{x^3 \log ^2(x)} \, dx\\ &=\frac {2 e^{4 x}}{3 x^2 \log (x)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.05, size = 16, normalized size = 1.00 \begin {gather*} \frac {2 e^{4 x}}{3 x^2 \log (x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.03, size = 14, normalized size = 0.88
method | result | size |
risch | \(\frac {2 \,{\mathrm e}^{4 x}}{3 \ln \left (x \right ) x^{2}}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 13, normalized size = 0.81 \begin {gather*} \frac {2 \, e^{\left (4 \, x\right )}}{3 \, x^{2} \log \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.42, size = 13, normalized size = 0.81 \begin {gather*} \frac {2 \, e^{\left (4 \, x\right )}}{3 \, x^{2} \log \left (x\right )} \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 = 0.88 \begin {gather*} \frac {2 e^{4 x}}{3 x^{2} \log {\left (x \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 13, normalized size = 0.81 \begin {gather*} \frac {2 \, e^{\left (4 \, x\right )}}{3 \, x^{2} \log \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 9.15, size = 13, normalized size = 0.81 \begin {gather*} \frac {2\,{\mathrm {e}}^{4\,x}}{3\,x^2\,\ln \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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