Optimal. Leaf size=19 \[ 1+\frac {1}{x+\frac {1}{3} \left (2 x+x^4+\log (5)\right )} \]
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Rubi [A] time = 0.10, antiderivative size = 13, normalized size of antiderivative = 0.68, number of steps used = 3, number of rules used = 2, integrand size = 40, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {2074, 2099} \begin {gather*} \frac {3}{x^4+5 x+\log (5)} \end {gather*}
Antiderivative was successfully verified.
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Rule 2074
Rule 2099
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {15}{\left (5 x+x^4+\log (5)\right )^2}-\frac {12 x^3}{\left (5 x+x^4+\log (5)\right )^2}\right ) \, dx\\ &=-\left (12 \int \frac {x^3}{\left (5 x+x^4+\log (5)\right )^2} \, dx\right )-15 \int \frac {1}{\left (5 x+x^4+\log (5)\right )^2} \, dx\\ &=\frac {3}{5 x+x^4+\log (5)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 13, normalized size = 0.68 \begin {gather*} \frac {3}{5 x+x^4+\log (5)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.00, size = 13, normalized size = 0.68 \begin {gather*} \frac {3}{x^{4} + 5 \, x + \log \relax (5)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.36, size = 13, normalized size = 0.68 \begin {gather*} \frac {3}{x^{4} + 5 \, x + \log \relax (5)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 14, normalized size = 0.74
method | result | size |
gosper | \(\frac {3}{x^{4}+\ln \relax (5)+5 x}\) | \(14\) |
default | \(\frac {3}{x^{4}+\ln \relax (5)+5 x}\) | \(14\) |
norman | \(\frac {3}{x^{4}+\ln \relax (5)+5 x}\) | \(14\) |
risch | \(\frac {3}{x^{4}+\ln \relax (5)+5 x}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.66, size = 13, normalized size = 0.68 \begin {gather*} \frac {3}{x^{4} + 5 \, x + \log \relax (5)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.11, size = 13, normalized size = 0.68 \begin {gather*} \frac {3}{x^4+5\,x+\ln \relax (5)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.35, size = 10, normalized size = 0.53 \begin {gather*} \frac {3}{x^{4} + 5 x + \log {\relax (5 )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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