Optimal. Leaf size=43 \[ \frac{201}{15125 (5 x+3)}-\frac{12}{1375 (5 x+3)^2}+\frac{20 \log (6-x)}{3993}+\frac{1493 \log (5 x+3)}{499125} \]
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Rubi [A] time = 0.0422541, antiderivative size = 43, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {1593, 148} \[ \frac{201}{15125 (5 x+3)}-\frac{12}{1375 (5 x+3)^2}+\frac{20 \log (6-x)}{3993}+\frac{1493 \log (5 x+3)}{499125} \]
Antiderivative was successfully verified.
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Rule 1593
Rule 148
Rubi steps
\begin{align*} \int \frac{-x^2+x^3}{(-6+x) (3+5 x)^3} \, dx &=\int \frac{(-1+x) x^2}{(-6+x) (3+5 x)^3} \, dx\\ &=\int \left (\frac{20}{3993 (-6+x)}+\frac{24}{275 (3+5 x)^3}-\frac{201}{3025 (3+5 x)^2}+\frac{1493}{99825 (3+5 x)}\right ) \, dx\\ &=-\frac{12}{1375 (3+5 x)^2}+\frac{201}{15125 (3+5 x)}+\frac{20 \log (6-x)}{3993}+\frac{1493 \log (3+5 x)}{499125}\\ \end{align*}
Mathematica [A] time = 0.0216479, size = 33, normalized size = 0.77 \[ \frac{\frac{99 (335 x+157)}{(5 x+3)^2}+2500 \log (x-6)+1493 \log (5 x+3)}{499125} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 34, normalized size = 0.8 \begin{align*} -{\frac{12}{1375\, \left ( 3+5\,x \right ) ^{2}}}+{\frac{201}{45375+75625\,x}}+{\frac{1493\,\ln \left ( 3+5\,x \right ) }{499125}}+{\frac{20\,\ln \left ( -6+x \right ) }{3993}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.92771, size = 46, normalized size = 1.07 \begin{align*} \frac{3 \,{\left (335 \, x + 157\right )}}{15125 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac{1493}{499125} \, \log \left (5 \, x + 3\right ) + \frac{20}{3993} \, \log \left (x - 6\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.92462, size = 170, normalized size = 3.95 \begin{align*} \frac{1493 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 2500 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (x - 6\right ) + 33165 \, x + 15543}{499125 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.141443, size = 32, normalized size = 0.74 \begin{align*} \frac{1005 x + 471}{378125 x^{2} + 453750 x + 136125} + \frac{20 \log{\left (x - 6 \right )}}{3993} + \frac{1493 \log{\left (x + \frac{3}{5} \right )}}{499125} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.07588, size = 42, normalized size = 0.98 \begin{align*} \frac{3 \,{\left (335 \, x + 157\right )}}{15125 \,{\left (5 \, x + 3\right )}^{2}} + \frac{1493}{499125} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) + \frac{20}{3993} \, \log \left ({\left | x - 6 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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