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 = 0.04, antiderivative size = 43, normalized size of antiderivative = 1.00, 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 148
Rule 1593
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*}
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Mathematica [A] time = 0.02, 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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fricas [A] time = 1.08, size = 53, normalized size = 1.23 \[ \frac {1493 \, {\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 2500 \, {\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (x - 6\right ) + 33165 \, x + 15543}{499125 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.18, size = 31, normalized size = 0.72 \[ \frac {3 \, {\left (335 \, x + 157\right )}}{15125 \, {\left (5 \, x + 3\right )}^{2}} + \frac {1493}{499125} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) + \frac {20}{3993} \, \log \left ({\left | x - 6 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 34, normalized size = 0.79 \[ \frac {1493 \ln \left (5 x +3\right )}{499125}+\frac {20 \ln \left (x -6\right )}{3993}-\frac {12}{1375 \left (5 x +3\right )^{2}}+\frac {201}{15125 \left (5 x +3\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.43, size = 34, normalized size = 0.79 \[ \frac {3 \, {\left (335 \, x + 157\right )}}{15125 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac {1493}{499125} \, \log \left (5 \, x + 3\right ) + \frac {20}{3993} \, \log \left (x - 6\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.12, size = 29, normalized size = 0.67 \[ \frac {20\,\ln \left (x-6\right )}{3993}+\frac {1493\,\ln \left (x+\frac {3}{5}\right )}{499125}+\frac {\frac {201\,x}{75625}+\frac {471}{378125}}{x^2+\frac {6\,x}{5}+\frac {9}{25}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 32, normalized size = 0.74 \[ \frac {1005 x + 471}{378125 x^{2} + 453750 x + 136125} + \frac {20 \log {\left (x - 6 \right )}}{3993} + \frac {1493 \log {\left (x + \frac {3}{5} \right )}}{499125} \]
Verification of antiderivative is not currently implemented for this CAS.
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