Optimal. Leaf size=30 \[ \frac {65 x}{27}-\frac {32 x^2}{9}+\frac {20 x^3}{9}-\frac {49}{81} \log (2+3 x) \]
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Rubi [A]
time = 0.01, antiderivative size = 30, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {78}
\begin {gather*} \frac {20 x^3}{9}-\frac {32 x^2}{9}+\frac {65 x}{27}-\frac {49}{81} \log (3 x+2) \end {gather*}
Antiderivative was successfully verified.
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Rule 78
Rubi steps
\begin {align*} \int \frac {(1-2 x)^2 (3+5 x)}{2+3 x} \, dx &=\int \left (\frac {65}{27}-\frac {64 x}{9}+\frac {20 x^2}{3}-\frac {49}{27 (2+3 x)}\right ) \, dx\\ &=\frac {65 x}{27}-\frac {32 x^2}{9}+\frac {20 x^3}{9}-\frac {49}{81} \log (2+3 x)\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 27, normalized size = 0.90 \begin {gather*} \frac {1}{243} \left (934+585 x-864 x^2+540 x^3-147 \log (2+3 x)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 23, normalized size = 0.77
method | result | size |
default | \(\frac {65 x}{27}-\frac {32 x^{2}}{9}+\frac {20 x^{3}}{9}-\frac {49 \ln \left (2+3 x \right )}{81}\) | \(23\) |
norman | \(\frac {65 x}{27}-\frac {32 x^{2}}{9}+\frac {20 x^{3}}{9}-\frac {49 \ln \left (2+3 x \right )}{81}\) | \(23\) |
risch | \(\frac {65 x}{27}-\frac {32 x^{2}}{9}+\frac {20 x^{3}}{9}-\frac {49 \ln \left (2+3 x \right )}{81}\) | \(23\) |
meijerg | \(-\frac {49 \ln \left (1+\frac {3 x}{2}\right )}{81}-\frac {7 x}{3}+\frac {8 x \left (-\frac {9 x}{2}+6\right )}{27}+\frac {20 x \left (9 x^{2}-9 x +12\right )}{81}\) | \(34\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 22, normalized size = 0.73 \begin {gather*} \frac {20}{9} \, x^{3} - \frac {32}{9} \, x^{2} + \frac {65}{27} \, x - \frac {49}{81} \, \log \left (3 \, x + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.59, size = 22, normalized size = 0.73 \begin {gather*} \frac {20}{9} \, x^{3} - \frac {32}{9} \, x^{2} + \frac {65}{27} \, x - \frac {49}{81} \, \log \left (3 \, x + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 27, normalized size = 0.90 \begin {gather*} \frac {20 x^{3}}{9} - \frac {32 x^{2}}{9} + \frac {65 x}{27} - \frac {49 \log {\left (3 x + 2 \right )}}{81} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.82, size = 23, normalized size = 0.77 \begin {gather*} \frac {20}{9} \, x^{3} - \frac {32}{9} \, x^{2} + \frac {65}{27} \, x - \frac {49}{81} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 20, normalized size = 0.67 \begin {gather*} \frac {65\,x}{27}-\frac {49\,\ln \left (x+\frac {2}{3}\right )}{81}-\frac {32\,x^2}{9}+\frac {20\,x^3}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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