Optimal. Leaf size=27 \[ -\frac {10 x}{9}+\frac {7}{27 (2+3 x)}+\frac {37}{27} \log (2+3 x) \]
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Rubi [A]
time = 0.01, antiderivative size = 27, 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 {10 x}{9}+\frac {7}{27 (3 x+2)}+\frac {37}{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)^2} \, dx &=\int \left (-\frac {10}{9}-\frac {7}{9 (2+3 x)^2}+\frac {37}{9 (2+3 x)}\right ) \, dx\\ &=-\frac {10 x}{9}+\frac {7}{27 (2+3 x)}+\frac {37}{27} \log (2+3 x)\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 26, normalized size = 0.96 \begin {gather*} \frac {1}{27} \left (-20-30 x+\frac {7}{2+3 x}+37 \log (2+3 x)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 22, normalized size = 0.81
method | result | size |
risch | \(-\frac {10 x}{9}+\frac {7}{81 \left (\frac {2}{3}+x \right )}+\frac {37 \ln \left (2+3 x \right )}{27}\) | \(20\) |
default | \(-\frac {10 x}{9}+\frac {7}{27 \left (2+3 x \right )}+\frac {37 \ln \left (2+3 x \right )}{27}\) | \(22\) |
norman | \(\frac {-\frac {47}{18} x -\frac {10}{3} x^{2}}{2+3 x}+\frac {37 \ln \left (2+3 x \right )}{27}\) | \(27\) |
meijerg | \(\frac {11 x}{12 \left (1+\frac {3 x}{2}\right )}+\frac {37 \ln \left (1+\frac {3 x}{2}\right )}{27}-\frac {10 x \left (\frac {9 x}{2}+6\right )}{27 \left (1+\frac {3 x}{2}\right )}\) | \(35\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.34, size = 21, normalized size = 0.78 \begin {gather*} -\frac {10}{9} \, x + \frac {7}{27 \, {\left (3 \, x + 2\right )}} + \frac {37}{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 = 0.51, size = 32, normalized size = 1.19 \begin {gather*} -\frac {90 \, x^{2} - 37 \, {\left (3 \, x + 2\right )} \log \left (3 \, x + 2\right ) + 60 \, x - 7}{27 \, {\left (3 \, x + 2\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 20, normalized size = 0.74 \begin {gather*} - \frac {10 x}{9} + \frac {37 \log {\left (3 x + 2 \right )}}{27} + \frac {7}{81 x + 54} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.26, size = 32, normalized size = 1.19 \begin {gather*} -\frac {10}{9} \, x + \frac {7}{27 \, {\left (3 \, x + 2\right )}} - \frac {37}{27} \, \log \left (\frac {{\left | 3 \, x + 2 \right |}}{3 \, {\left (3 \, x + 2\right )}^{2}}\right ) - \frac {20}{27} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.10, size = 19, normalized size = 0.70 \begin {gather*} \frac {37\,\ln \left (x+\frac {2}{3}\right )}{27}-\frac {10\,x}{9}+\frac {7}{81\,\left (x+\frac {2}{3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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