Optimal. Leaf size=34 \[ \frac {33 x}{125}-\frac {9 x^2}{25}-\frac {11}{625 (3+5 x)}+\frac {64}{625} \log (3+5 x) \]
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Rubi [A]
time = 0.01, antiderivative size = 34, 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 {9 x^2}{25}+\frac {33 x}{125}-\frac {11}{625 (5 x+3)}+\frac {64}{625} \log (5 x+3) \end {gather*}
Antiderivative was successfully verified.
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Rule 78
Rubi steps
\begin {align*} \int \frac {(1-2 x) (2+3 x)^2}{(3+5 x)^2} \, dx &=\int \left (\frac {33}{125}-\frac {18 x}{25}+\frac {11}{125 (3+5 x)^2}+\frac {64}{125 (3+5 x)}\right ) \, dx\\ &=\frac {33 x}{125}-\frac {9 x^2}{25}-\frac {11}{625 (3+5 x)}+\frac {64}{625} \log (3+5 x)\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 41, normalized size = 1.21 \begin {gather*} \frac {619+1545 x+150 x^2-1125 x^3+64 (3+5 x) \log (-3 (3+5 x))}{625 (3+5 x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 27, normalized size = 0.79
method | result | size |
risch | \(-\frac {9 x^{2}}{25}+\frac {33 x}{125}-\frac {11}{3125 \left (x +\frac {3}{5}\right )}+\frac {64 \ln \left (3+5 x \right )}{625}\) | \(25\) |
default | \(\frac {33 x}{125}-\frac {9 x^{2}}{25}-\frac {11}{625 \left (3+5 x \right )}+\frac {64 \ln \left (3+5 x \right )}{625}\) | \(27\) |
norman | \(\frac {\frac {308}{375} x +\frac {6}{25} x^{2}-\frac {9}{5} x^{3}}{3+5 x}+\frac {64 \ln \left (3+5 x \right )}{625}\) | \(32\) |
meijerg | \(\frac {8 x}{45 \left (1+\frac {5 x}{3}\right )}+\frac {64 \ln \left (1+\frac {5 x}{3}\right )}{625}-\frac {x \left (5 x +6\right )}{5 \left (1+\frac {5 x}{3}\right )}+\frac {27 x \left (-\frac {50}{9} x^{2}+10 x +12\right )}{250 \left (1+\frac {5 x}{3}\right )}\) | \(55\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.38, size = 26, normalized size = 0.76 \begin {gather*} -\frac {9}{25} \, x^{2} + \frac {33}{125} \, x - \frac {11}{625 \, {\left (5 \, x + 3\right )}} + \frac {64}{625} \, \log \left (5 \, x + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 1.67, size = 37, normalized size = 1.09 \begin {gather*} -\frac {1125 \, x^{3} - 150 \, x^{2} - 64 \, {\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 495 \, x + 11}{625 \, {\left (5 \, x + 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 27, normalized size = 0.79 \begin {gather*} - \frac {9 x^{2}}{25} + \frac {33 x}{125} + \frac {64 \log {\left (5 x + 3 \right )}}{625} - \frac {11}{3125 x + 1875} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.06, size = 48, normalized size = 1.41 \begin {gather*} \frac {3}{625} \, {\left (5 \, x + 3\right )}^{2} {\left (\frac {29}{5 \, x + 3} - 3\right )} - \frac {11}{625 \, {\left (5 \, x + 3\right )}} - \frac {64}{625} \, \log \left (\frac {{\left | 5 \, x + 3 \right |}}{5 \, {\left (5 \, x + 3\right )}^{2}}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 24, normalized size = 0.71 \begin {gather*} \frac {33\,x}{125}+\frac {64\,\ln \left (x+\frac {3}{5}\right )}{625}-\frac {11}{3125\,\left (x+\frac {3}{5}\right )}-\frac {9\,x^2}{25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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