Optimal. Leaf size=55 \[ \frac {5459 x}{3125}-\frac {3621 x^2}{3125}-\frac {1809 x^3}{625}+\frac {189 x^4}{125}+\frac {324 x^5}{125}-\frac {121}{78125 (3+5 x)}+\frac {1408 \log (3+5 x)}{78125} \]
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Rubi [A]
time = 0.02, antiderivative size = 55, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {90}
\begin {gather*} \frac {324 x^5}{125}+\frac {189 x^4}{125}-\frac {1809 x^3}{625}-\frac {3621 x^2}{3125}+\frac {5459 x}{3125}-\frac {121}{78125 (5 x+3)}+\frac {1408 \log (5 x+3)}{78125} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {(1-2 x)^2 (2+3 x)^4}{(3+5 x)^2} \, dx &=\int \left (\frac {5459}{3125}-\frac {7242 x}{3125}-\frac {5427 x^2}{625}+\frac {756 x^3}{125}+\frac {324 x^4}{25}+\frac {121}{15625 (3+5 x)^2}+\frac {1408}{15625 (3+5 x)}\right ) \, dx\\ &=\frac {5459 x}{3125}-\frac {3621 x^2}{3125}-\frac {1809 x^3}{625}+\frac {189 x^4}{125}+\frac {324 x^5}{125}-\frac {121}{78125 (3+5 x)}+\frac {1408 \log (3+5 x)}{78125}\\ \end {align*}
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Mathematica [A]
time = 0.03, size = 56, normalized size = 1.02 \begin {gather*} \frac {990421+3698835 x+2054000 x^2-5655000 x^3-3881250 x^4+5990625 x^5+5062500 x^6+7040 (3+5 x) \log (6 (3+5 x))}{390625 (3+5 x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 42, normalized size = 0.76
method | result | size |
risch | \(\frac {324 x^{5}}{125}+\frac {189 x^{4}}{125}-\frac {1809 x^{3}}{625}-\frac {3621 x^{2}}{3125}+\frac {5459 x}{3125}-\frac {121}{390625 \left (x +\frac {3}{5}\right )}+\frac {1408 \ln \left (3+5 x \right )}{78125}\) | \(40\) |
default | \(\frac {5459 x}{3125}-\frac {3621 x^{2}}{3125}-\frac {1809 x^{3}}{625}+\frac {189 x^{4}}{125}+\frac {324 x^{5}}{125}-\frac {121}{78125 \left (3+5 x \right )}+\frac {1408 \ln \left (3+5 x \right )}{78125}\) | \(42\) |
norman | \(\frac {\frac {245776}{46875} x +\frac {16432}{3125} x^{2}-\frac {9048}{625} x^{3}-\frac {1242}{125} x^{4}+\frac {1917}{125} x^{5}+\frac {324}{25} x^{6}}{3+5 x}+\frac {1408 \ln \left (3+5 x \right )}{78125}\) | \(47\) |
meijerg | \(-\frac {16 x}{45 \left (1+\frac {5 x}{3}\right )}+\frac {1408 \ln \left (1+\frac {5 x}{3}\right )}{78125}-\frac {104 x \left (5 x +6\right )}{75 \left (1+\frac {5 x}{3}\right )}+\frac {198 x \left (-\frac {50}{9} x^{2}+10 x +12\right )}{125 \left (1+\frac {5 x}{3}\right )}+\frac {243 x \left (\frac {625}{27} x^{3}-\frac {250}{9} x^{2}+50 x +60\right )}{3125 \left (1+\frac {5 x}{3}\right )}-\frac {243 x \left (-\frac {625}{27} x^{4}+\frac {625}{27} x^{3}-\frac {250}{9} x^{2}+50 x +60\right )}{625 \left (1+\frac {5 x}{3}\right )}+\frac {13122 x \left (\frac {43750}{243} x^{5}-\frac {4375}{27} x^{4}+\frac {4375}{27} x^{3}-\frac {1750}{9} x^{2}+350 x +420\right )}{546875 \left (1+\frac {5 x}{3}\right )}\) | \(145\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 41, normalized size = 0.75 \begin {gather*} \frac {324}{125} \, x^{5} + \frac {189}{125} \, x^{4} - \frac {1809}{625} \, x^{3} - \frac {3621}{3125} \, x^{2} + \frac {5459}{3125} \, x - \frac {121}{78125 \, {\left (5 \, x + 3\right )}} + \frac {1408}{78125} \, \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 = 0.43, size = 52, normalized size = 0.95 \begin {gather*} \frac {1012500 \, x^{6} + 1198125 \, x^{5} - 776250 \, x^{4} - 1131000 \, x^{3} + 410800 \, x^{2} + 1408 \, {\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 409425 \, x - 121}{78125 \, {\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 = 48, normalized size = 0.87 \begin {gather*} \frac {324 x^{5}}{125} + \frac {189 x^{4}}{125} - \frac {1809 x^{3}}{625} - \frac {3621 x^{2}}{3125} + \frac {5459 x}{3125} + \frac {1408 \log {\left (5 x + 3 \right )}}{78125} - \frac {121}{390625 x + 234375} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.41, size = 75, normalized size = 1.36 \begin {gather*} -\frac {1}{390625} \, {\left (5 \, x + 3\right )}^{5} {\left (\frac {3915}{5 \, x + 3} - \frac {8775}{{\left (5 \, x + 3\right )}^{2}} - \frac {26850}{{\left (5 \, x + 3\right )}^{3}} - \frac {30050}{{\left (5 \, x + 3\right )}^{4}} - 324\right )} - \frac {121}{78125 \, {\left (5 \, x + 3\right )}} - \frac {1408}{78125} \, \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 = 39, normalized size = 0.71 \begin {gather*} \frac {5459\,x}{3125}+\frac {1408\,\ln \left (x+\frac {3}{5}\right )}{78125}-\frac {121}{390625\,\left (x+\frac {3}{5}\right )}-\frac {3621\,x^2}{3125}-\frac {1809\,x^3}{625}+\frac {189\,x^4}{125}+\frac {324\,x^5}{125} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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