Optimal. Leaf size=30 \[ -2+\frac {x}{x-(3-x) \log \left (-3+\frac {50-x}{2 x}\right )} \]
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Rubi [A]
time = 0.25, antiderivative size = 25, normalized size of antiderivative = 0.83, number of steps
used = 3, number of rules used = 3, integrand size = 97, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.031, Rules used = {6820, 6843, 32}
\begin {gather*} -\frac {1}{\frac {x}{(x-3) \log \left (\frac {25}{x}-\frac {7}{2}\right )}+1} \end {gather*}
Antiderivative was successfully verified.
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Rule 32
Rule 6820
Rule 6843
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {50 (-3+x)+3 (-50+7 x) \log \left (-\frac {7}{2}+\frac {25}{x}\right )}{(50-7 x) \left (x+(-3+x) \log \left (-\frac {7}{2}+\frac {25}{x}\right )\right )^2} \, dx\\ &=\text {Subst}\left (\int \frac {1}{(1+x)^2} \, dx,x,\frac {x}{(-3+x) \log \left (-\frac {7}{2}+\frac {25}{x}\right )}\right )\\ &=-\frac {1}{1+\frac {x}{(-3+x) \log \left (-\frac {7}{2}+\frac {25}{x}\right )}}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.07, size = 20, normalized size = 0.67 \begin {gather*} \frac {x}{x+(-3+x) \log \left (-\frac {7}{2}+\frac {25}{x}\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 2.17, size = 34, normalized size = 1.13
method | result | size |
norman | \(\frac {x}{\ln \left (\frac {-7 x +50}{2 x}\right ) x +x -3 \ln \left (\frac {-7 x +50}{2 x}\right )}\) | \(33\) |
risch | \(\frac {x}{\ln \left (\frac {-7 x +50}{2 x}\right ) x +x -3 \ln \left (\frac {-7 x +50}{2 x}\right )}\) | \(33\) |
derivativedivides | \(-\frac {50}{6 \left (-\frac {7}{2}+\frac {25}{x}\right ) \ln \left (-\frac {7}{2}+\frac {25}{x}\right )-29 \ln \left (-\frac {7}{2}+\frac {25}{x}\right )-50}\) | \(34\) |
default | \(-\frac {50}{6 \left (-\frac {7}{2}+\frac {25}{x}\right ) \ln \left (-\frac {7}{2}+\frac {25}{x}\right )-29 \ln \left (-\frac {7}{2}+\frac {25}{x}\right )-50}\) | \(34\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.52, size = 33, normalized size = 1.10 \begin {gather*} -\frac {x}{x {\left (\log \left (2\right ) - 1\right )} + {\left (x - 3\right )} \log \left (x\right ) - {\left (x - 3\right )} \log \left (-7 \, x + 50\right ) - 3 \, \log \left (2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 21, normalized size = 0.70 \begin {gather*} \frac {x}{{\left (x - 3\right )} \log \left (-\frac {7 \, x - 50}{2 \, x}\right ) + x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.08, size = 15, normalized size = 0.50 \begin {gather*} \frac {x}{x + \left (x - 3\right ) \log {\left (\frac {25 - \frac {7 x}{2}}{x} \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.43, size = 40, normalized size = 1.33 \begin {gather*} \frac {50}{\frac {3 \, {\left (7 \, x - 50\right )} \log \left (-\frac {7 \, x - 50}{2 \, x}\right )}{x} + 29 \, \log \left (-\frac {7 \, x - 50}{2 \, x}\right ) + 50} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.92, size = 21, normalized size = 0.70 \begin {gather*} \frac {x}{x+\ln \left (-\frac {7\,x-50}{2\,x}\right )\,\left (x-3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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