Optimal. Leaf size=54 \[ \frac{x^4}{16}+\frac{7 x^3}{60}-\frac{49 x^2}{200}+\frac{1}{4} x^4 \log \left (\frac{5 x+7}{x^2}\right )+\frac{343 x}{500}-\frac{2401 \log (5 x+7)}{2500} \]
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Rubi [A] time = 0.0392872, antiderivative size = 54, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.214, Rules used = {2495, 30, 43} \[ \frac{x^4}{16}+\frac{7 x^3}{60}-\frac{49 x^2}{200}+\frac{1}{4} x^4 \log \left (\frac{5 x+7}{x^2}\right )+\frac{343 x}{500}-\frac{2401 \log (5 x+7)}{2500} \]
Antiderivative was successfully verified.
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Rule 2495
Rule 30
Rule 43
Rubi steps
\begin{align*} \int x^3 \log \left (\frac{7+5 x}{x^2}\right ) \, dx &=\frac{1}{4} x^4 \log \left (\frac{7+5 x}{x^2}\right )+\frac{\int x^3 \, dx}{2}-\frac{5}{4} \int \frac{x^4}{7+5 x} \, dx\\ &=\frac{x^4}{8}+\frac{1}{4} x^4 \log \left (\frac{7+5 x}{x^2}\right )-\frac{5}{4} \int \left (-\frac{343}{625}+\frac{49 x}{125}-\frac{7 x^2}{25}+\frac{x^3}{5}+\frac{2401}{625 (7+5 x)}\right ) \, dx\\ &=\frac{343 x}{500}-\frac{49 x^2}{200}+\frac{7 x^3}{60}+\frac{x^4}{16}-\frac{2401 \log (7+5 x)}{2500}+\frac{1}{4} x^4 \log \left (\frac{7+5 x}{x^2}\right )\\ \end{align*}
Mathematica [A] time = 0.0127958, size = 54, normalized size = 1. \[ \frac{x^4}{16}+\frac{7 x^3}{60}-\frac{49 x^2}{200}+\frac{1}{4} x^4 \log \left (\frac{5 x+7}{x^2}\right )+\frac{343 x}{500}-\frac{2401 \log (5 x+7)}{2500} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.016, size = 53, normalized size = 1. \begin{align*}{\frac{{x}^{4}}{4}\ln \left ({\frac{1}{x} \left ( 7\,{x}^{-1}+5 \right ) } \right ) }-{\frac{2401}{2500}\ln \left ( 7\,{x}^{-1}+5 \right ) }+{\frac{{x}^{4}}{16}}+{\frac{7\,{x}^{3}}{60}}-{\frac{49\,{x}^{2}}{200}}+{\frac{343\,x}{500}}+{\frac{2401\,\ln \left ({x}^{-1} \right ) }{2500}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.05635, size = 57, normalized size = 1.06 \begin{align*} \frac{1}{4} \, x^{4} \log \left (\frac{5 \, x + 7}{x^{2}}\right ) + \frac{1}{16} \, x^{4} + \frac{7}{60} \, x^{3} - \frac{49}{200} \, x^{2} + \frac{343}{500} \, x - \frac{2401}{2500} \, \log \left (5 \, x + 7\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.86796, size = 135, normalized size = 2.5 \begin{align*} \frac{1}{4} \, x^{4} \log \left (\frac{5 \, x + 7}{x^{2}}\right ) + \frac{1}{16} \, x^{4} + \frac{7}{60} \, x^{3} - \frac{49}{200} \, x^{2} + \frac{343}{500} \, x - \frac{2401}{2500} \, \log \left (5 \, x + 7\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.149822, size = 48, normalized size = 0.89 \begin{align*} \frac{x^{4} \log{\left (\frac{5 x + 7}{x^{2}} \right )}}{4} + \frac{x^{4}}{16} + \frac{7 x^{3}}{60} - \frac{49 x^{2}}{200} + \frac{343 x}{500} - \frac{2401 \log{\left (5 x + 7 \right )}}{2500} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.27232, size = 58, normalized size = 1.07 \begin{align*} \frac{1}{4} \, x^{4} \log \left (\frac{5 \, x + 7}{x^{2}}\right ) + \frac{1}{16} \, x^{4} + \frac{7}{60} \, x^{3} - \frac{49}{200} \, x^{2} + \frac{343}{500} \, x - \frac{2401}{2500} \, \log \left ({\left | 5 \, x + 7 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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