Optimal. Leaf size=23 \[ \frac {17 x}{9}-\frac {5 x^2}{3}-\frac {7}{27} \log (2+3 x) \]
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Rubi [A]
time = 0.01, antiderivative size = 23, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {78}
\begin {gather*} -\frac {5 x^2}{3}+\frac {17 x}{9}-\frac {7}{27} \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) (3+5 x)}{2+3 x} \, dx &=\int \left (\frac {17}{9}-\frac {10 x}{3}-\frac {7}{9 (2+3 x)}\right ) \, dx\\ &=\frac {17 x}{9}-\frac {5 x^2}{3}-\frac {7}{27} \log (2+3 x)\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 22, normalized size = 0.96 \begin {gather*} \frac {1}{27} \left (54+51 x-45 x^2-7 \log (2+3 x)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 18, normalized size = 0.78
method | result | size |
default | \(\frac {17 x}{9}-\frac {5 x^{2}}{3}-\frac {7 \ln \left (2+3 x \right )}{27}\) | \(18\) |
norman | \(\frac {17 x}{9}-\frac {5 x^{2}}{3}-\frac {7 \ln \left (2+3 x \right )}{27}\) | \(18\) |
risch | \(\frac {17 x}{9}-\frac {5 x^{2}}{3}-\frac {7 \ln \left (2+3 x \right )}{27}\) | \(18\) |
meijerg | \(-\frac {7 \ln \left (1+\frac {3 x}{2}\right )}{27}-\frac {x}{3}+\frac {10 x \left (-\frac {9 x}{2}+6\right )}{27}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 17, normalized size = 0.74 \begin {gather*} -\frac {5}{3} \, x^{2} + \frac {17}{9} \, x - \frac {7}{27} \, \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 = 0.55, size = 17, normalized size = 0.74 \begin {gather*} -\frac {5}{3} \, x^{2} + \frac {17}{9} \, x - \frac {7}{27} \, \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 = 20, normalized size = 0.87 \begin {gather*} - \frac {5 x^{2}}{3} + \frac {17 x}{9} - \frac {7 \log {\left (3 x + 2 \right )}}{27} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.90, size = 18, normalized size = 0.78 \begin {gather*} -\frac {5}{3} \, x^{2} + \frac {17}{9} \, x - \frac {7}{27} \, \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 = 15, normalized size = 0.65 \begin {gather*} \frac {17\,x}{9}-\frac {7\,\ln \left (x+\frac {2}{3}\right )}{27}-\frac {5\,x^2}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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