Optimal. Leaf size=41 \[ \frac {522 x}{625}-\frac {81 x^2}{250}-\frac {18 x^3}{25}-\frac {11}{3125 (3+5 x)}+\frac {97 \log (3+5 x)}{3125} \]
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Rubi [A]
time = 0.01, antiderivative size = 41, 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 {18 x^3}{25}-\frac {81 x^2}{250}+\frac {522 x}{625}-\frac {11}{3125 (5 x+3)}+\frac {97 \log (5 x+3)}{3125} \end {gather*}
Antiderivative was successfully verified.
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Rule 78
Rubi steps
\begin {align*} \int \frac {(1-2 x) (2+3 x)^3}{(3+5 x)^2} \, dx &=\int \left (\frac {522}{625}-\frac {81 x}{125}-\frac {54 x^2}{25}+\frac {11}{625 (3+5 x)^2}+\frac {97}{625 (3+5 x)}\right ) \, dx\\ &=\frac {522 x}{625}-\frac {81 x^2}{250}-\frac {18 x^3}{25}-\frac {11}{3125 (3+5 x)}+\frac {97 \log (3+5 x)}{3125}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 46, normalized size = 1.12 \begin {gather*} \frac {27354+92680 x+60075 x^2-70875 x^3-67500 x^4+582 (3+5 x) \log (-3 (3+5 x))}{18750 (3+5 x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 32, normalized size = 0.78
method | result | size |
risch | \(-\frac {18 x^{3}}{25}-\frac {81 x^{2}}{250}+\frac {522 x}{625}-\frac {11}{15625 \left (x +\frac {3}{5}\right )}+\frac {97 \ln \left (3+5 x \right )}{3125}\) | \(30\) |
default | \(\frac {522 x}{625}-\frac {81 x^{2}}{250}-\frac {18 x^{3}}{25}-\frac {11}{3125 \left (3+5 x \right )}+\frac {97 \ln \left (3+5 x \right )}{3125}\) | \(32\) |
norman | \(\frac {\frac {4709}{1875} x +\frac {801}{250} x^{2}-\frac {189}{50} x^{3}-\frac {18}{5} x^{4}}{3+5 x}+\frac {97 \ln \left (3+5 x \right )}{3125}\) | \(37\) |
meijerg | \(-\frac {4 x}{9 \left (1+\frac {5 x}{3}\right )}+\frac {97 \ln \left (1+\frac {5 x}{3}\right )}{3125}-\frac {6 x \left (5 x +6\right )}{25 \left (1+\frac {5 x}{3}\right )}+\frac {243 x \left (-\frac {50}{9} x^{2}+10 x +12\right )}{500 \left (1+\frac {5 x}{3}\right )}-\frac {162 x \left (\frac {625}{27} x^{3}-\frac {250}{9} x^{2}+50 x +60\right )}{3125 \left (1+\frac {5 x}{3}\right )}\) | \(80\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.32, size = 31, normalized size = 0.76 \begin {gather*} -\frac {18}{25} \, x^{3} - \frac {81}{250} \, x^{2} + \frac {522}{625} \, x - \frac {11}{3125 \, {\left (5 \, x + 3\right )}} + \frac {97}{3125} \, \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 = 1.23, size = 42, normalized size = 1.02 \begin {gather*} -\frac {22500 \, x^{4} + 23625 \, x^{3} - 20025 \, x^{2} - 194 \, {\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 15660 \, x + 22}{6250 \, {\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 = 34, normalized size = 0.83 \begin {gather*} - \frac {18 x^{3}}{25} - \frac {81 x^{2}}{250} + \frac {522 x}{625} + \frac {97 \log {\left (5 x + 3 \right )}}{3125} - \frac {11}{15625 x + 9375} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.06, size = 57, normalized size = 1.39 \begin {gather*} \frac {9}{6250} \, {\left (5 \, x + 3\right )}^{3} {\left (\frac {27}{5 \, x + 3} + \frac {62}{{\left (5 \, x + 3\right )}^{2}} - 4\right )} - \frac {11}{3125 \, {\left (5 \, x + 3\right )}} - \frac {97}{3125} \, \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 = 29, normalized size = 0.71 \begin {gather*} \frac {522\,x}{625}+\frac {97\,\ln \left (x+\frac {3}{5}\right )}{3125}-\frac {11}{15625\,\left (x+\frac {3}{5}\right )}-\frac {81\,x^2}{250}-\frac {18\,x^3}{25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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