Optimal. Leaf size=17 \[ 6 \log \left (\frac {x^2}{(4+x) (625+x)}\right ) \]
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Rubi [A]
time = 0.03, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps
used = 4, number of rules used = 3, integrand size = 32, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.094, Rules used = {2023, 1608,
814} \begin {gather*} 12 \log (x)-6 \log (x+4)-6 \log (x+625) \end {gather*}
Antiderivative was successfully verified.
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Rule 814
Rule 1608
Rule 2023
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {30000+3774 x}{2500 x+629 x^2+x^3} \, dx\\ &=\int \frac {30000+3774 x}{x \left (2500+629 x+x^2\right )} \, dx\\ &=\int \left (\frac {12}{x}-\frac {6}{4+x}-\frac {6}{625+x}\right ) \, dx\\ &=12 \log (x)-6 \log (4+x)-6 \log (625+x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 18, normalized size = 1.06 \begin {gather*} 6 \left (2 \log (x)-\log \left (2500+629 x+x^2\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 18, normalized size = 1.06
method | result | size |
risch | \(12 \ln \left (x \right )-6 \ln \left (x^{2}+629 x +2500\right )\) | \(17\) |
default | \(12 \ln \left (x \right )-6 \ln \left (x +625\right )-6 \ln \left (4+x \right )\) | \(18\) |
norman | \(12 \ln \left (x \right )-6 \ln \left (x +625\right )-6 \ln \left (4+x \right )\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.33, size = 17, normalized size = 1.00 \begin {gather*} -6 \, \log \left (x + 625\right ) - 6 \, \log \left (x + 4\right ) + 12 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.41, size = 16, normalized size = 0.94 \begin {gather*} -6 \, \log \left (x^{2} + 629 \, x + 2500\right ) + 12 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 15, normalized size = 0.88 \begin {gather*} 12 \log {\left (x \right )} - 6 \log {\left (x^{2} + 629 x + 2500 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 20, normalized size = 1.18 \begin {gather*} -6 \, \log \left ({\left | x + 625 \right |}\right ) - 6 \, \log \left ({\left | x + 4 \right |}\right ) + 12 \, \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.16, size = 16, normalized size = 0.94 \begin {gather*} 12\,\ln \left (x\right )-6\,\ln \left (x^2+629\,x+2500\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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