Optimal. Leaf size=17 \[ 4+\frac {x}{x+\frac {25 x}{\log \left (x^2\right )}} \]
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Rubi [A]
time = 0.01, antiderivative size = 10, normalized size of antiderivative = 0.59, number of steps
used = 3, number of rules used = 2, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.087, Rules used = {12, 32}
\begin {gather*} -\frac {25}{\log \left (x^2\right )+25} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 32
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=50 \int \frac {1}{625 x+50 x \log \left (x^2\right )+x \log ^2\left (x^2\right )} \, dx\\ &=25 \text {Subst}\left (\int \frac {1}{(25+x)^2} \, dx,x,\log \left (x^2\right )\right )\\ &=-\frac {25}{25+\log \left (x^2\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 10, normalized size = 0.59 \begin {gather*} -\frac {25}{25+\log \left (x^2\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.07, size = 11, normalized size = 0.65
method | result | size |
default | \(-\frac {25}{\ln \left (x^{2}\right )+25}\) | \(11\) |
norman | \(-\frac {25}{\ln \left (x^{2}\right )+25}\) | \(11\) |
risch | \(-\frac {25}{\ln \left (x^{2}\right )+25}\) | \(11\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 10, normalized size = 0.59 \begin {gather*} -\frac {25}{2 \, \log \left (x\right ) + 25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 10, normalized size = 0.59 \begin {gather*} -\frac {25}{\log \left (x^{2}\right ) + 25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 8, normalized size = 0.47 \begin {gather*} - \frac {25}{\log {\left (x^{2} \right )} + 25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 10, normalized size = 0.59 \begin {gather*} -\frac {25}{\log \left (x^{2}\right ) + 25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.08, size = 10, normalized size = 0.59 \begin {gather*} -\frac {25}{\ln \left (x^2\right )+25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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