Optimal. Leaf size=10 \[ \log ^2\left (-\frac {1}{5+x}\right ) \]
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Rubi [A] time = 0.02, antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {12, 2390, 2301} \begin {gather*} \log ^2\left (-\frac {1}{x+5}\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2301
Rule 2390
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\left (2 \int \frac {\log \left (-\frac {1}{5+x}\right )}{5+x} \, dx\right )\\ &=-\left (2 \operatorname {Subst}\left (\int \frac {\log \left (-\frac {1}{x}\right )}{x} \, dx,x,5+x\right )\right )\\ &=\log ^2\left (-\frac {1}{5+x}\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 10, normalized size = 1.00 \begin {gather*} \log ^2\left (-\frac {1}{5+x}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.57, size = 10, normalized size = 1.00 \begin {gather*} \log \left (-\frac {1}{x + 5}\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 10, normalized size = 1.00 \begin {gather*} \log \left (-\frac {1}{x + 5}\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 11, normalized size = 1.10
method | result | size |
derivativedivides | \(\ln \left (-\frac {1}{5+x}\right )^{2}\) | \(11\) |
default | \(\ln \left (-\frac {1}{5+x}\right )^{2}\) | \(11\) |
norman | \(\ln \left (-\frac {1}{5+x}\right )^{2}\) | \(11\) |
risch | \(\ln \left (-\frac {1}{5+x}\right )^{2}\) | \(11\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.37, size = 23, normalized size = 2.30 \begin {gather*} -\log \left (x + 5\right )^{2} - 2 \, \log \left (x + 5\right ) \log \left (-\frac {1}{x + 5}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.55, size = 10, normalized size = 1.00 \begin {gather*} {\ln \left (-\frac {1}{x+5}\right )}^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 8, normalized size = 0.80 \begin {gather*} \log {\left (- \frac {1}{x + 5} \right )}^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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