Optimal. Leaf size=22 \[ \frac {5 x (-1+5 x)+\frac {e^3 \log (5)}{x}}{x^2} \]
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Rubi [A]
time = 0.01, antiderivative size = 15, normalized size of antiderivative = 0.68, number of steps
used = 2, number of rules used = 1, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {14}
\begin {gather*} \frac {e^3 \log (5)}{x^3}-\frac {5}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {5}{x^2}-\frac {3 e^3 \log (5)}{x^4}\right ) \, dx\\ &=-\frac {5}{x}+\frac {e^3 \log (5)}{x^3}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 15, normalized size = 0.68 \begin {gather*} -\frac {5}{x}+\frac {e^3 \log (5)}{x^3} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.15, size = 15, normalized size = 0.68
method | result | size |
default | \(\frac {{\mathrm e}^{3} \ln \left (5\right )}{x^{3}}-\frac {5}{x}\) | \(15\) |
gosper | \(\frac {{\mathrm e}^{3} \ln \left (5\right )-5 x^{2}}{x^{3}}\) | \(16\) |
norman | \(\frac {{\mathrm e}^{3} \ln \left (5\right )-5 x^{2}}{x^{3}}\) | \(16\) |
risch | \(\frac {{\mathrm e}^{3} \ln \left (5\right )-5 x^{2}}{x^{3}}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 17, normalized size = 0.77 \begin {gather*} -\frac {5 \, x^{2} - e^{3} \log \left (5\right )}{x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 17, normalized size = 0.77 \begin {gather*} -\frac {5 \, x^{2} - e^{3} \log \left (5\right )}{x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 14, normalized size = 0.64 \begin {gather*} \frac {- 5 x^{2} + e^{3} \log {\left (5 \right )}}{x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 17, normalized size = 0.77 \begin {gather*} -\frac {5 \, x^{2} - e^{3} \log \left (5\right )}{x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.07, size = 15, normalized size = 0.68 \begin {gather*} \frac {{\mathrm {e}}^3\,\ln \left (5\right )-5\,x^2}{x^3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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