Optimal. Leaf size=28 \[ x \left (-\frac {e^{6-4 x}}{25 x^4}+x\right )-\log \left (\frac {4}{\log (4)}\right ) \]
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Rubi [A] time = 0.07, antiderivative size = 18, normalized size of antiderivative = 0.64, number of steps used = 4, number of rules used = 3, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.115, Rules used = {12, 14, 2197} \begin {gather*} x^2-\frac {e^{6-4 x}}{25 x^3} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2197
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{25} \int \frac {50 x^5+e^{6-4 x} (3+4 x)}{x^4} \, dx\\ &=\frac {1}{25} \int \left (50 x+\frac {e^{6-4 x} (3+4 x)}{x^4}\right ) \, dx\\ &=x^2+\frac {1}{25} \int \frac {e^{6-4 x} (3+4 x)}{x^4} \, dx\\ &=-\frac {e^{6-4 x}}{25 x^3}+x^2\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 18, normalized size = 0.64 \begin {gather*} -\frac {e^{6-4 x}}{25 x^3}+x^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.98, size = 19, normalized size = 0.68 \begin {gather*} \frac {25 \, x^{5} - e^{\left (-4 \, x + 6\right )}}{25 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.28, size = 19, normalized size = 0.68 \begin {gather*} \frac {25 \, x^{5} - e^{\left (-4 \, x + 6\right )}}{25 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 16, normalized size = 0.57
method | result | size |
risch | \(x^{2}-\frac {{\mathrm e}^{6-4 x}}{25 x^{3}}\) | \(16\) |
norman | \(\frac {x^{5}-\frac {{\mathrm e}^{6-4 x}}{25}}{x^{3}}\) | \(19\) |
derivativedivides | \(-\frac {9}{2}+3 x +\frac {\left (3-2 x \right )^{2}}{4}-\frac {{\mathrm e}^{6-4 x}}{25 x^{3}}\) | \(28\) |
default | \(-\frac {9}{2}+3 x +\frac {\left (3-2 x \right )^{2}}{4}-\frac {{\mathrm e}^{6-4 x}}{25 x^{3}}\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.46, size = 22, normalized size = 0.79 \begin {gather*} x^{2} - \frac {64}{25} \, e^{6} \Gamma \left (-2, 4 \, x\right ) - \frac {192}{25} \, e^{6} \Gamma \left (-3, 4 \, x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.83, size = 15, normalized size = 0.54 \begin {gather*} x^2-\frac {{\mathrm {e}}^{-4\,x}\,{\mathrm {e}}^6}{25\,x^3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 14, normalized size = 0.50 \begin {gather*} x^{2} - \frac {e^{6 - 4 x}}{25 x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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