Optimal. Leaf size=62 \[ \frac {555489 x}{78125}+\frac {40743 x^2}{3125}+\frac {5553 x^3}{3125}-\frac {14094 x^4}{625}-\frac {16767 x^5}{625}-\frac {243 x^6}{25}-\frac {11}{390625 (3+5 x)}+\frac {196 \log (3+5 x)}{390625} \]
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Rubi [A]
time = 0.02, antiderivative size = 62, 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 {243 x^6}{25}-\frac {16767 x^5}{625}-\frac {14094 x^4}{625}+\frac {5553 x^3}{3125}+\frac {40743 x^2}{3125}+\frac {555489 x}{78125}-\frac {11}{390625 (5 x+3)}+\frac {196 \log (5 x+3)}{390625} \end {gather*}
Antiderivative was successfully verified.
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Rule 78
Rubi steps
\begin {align*} \int \frac {(1-2 x) (2+3 x)^6}{(3+5 x)^2} \, dx &=\int \left (\frac {555489}{78125}+\frac {81486 x}{3125}+\frac {16659 x^2}{3125}-\frac {56376 x^3}{625}-\frac {16767 x^4}{125}-\frac {1458 x^5}{25}+\frac {11}{78125 (3+5 x)^2}+\frac {196}{78125 (3+5 x)}\right ) \, dx\\ &=\frac {555489 x}{78125}+\frac {40743 x^2}{3125}+\frac {5553 x^3}{3125}-\frac {14094 x^4}{625}-\frac {16767 x^5}{625}-\frac {243 x^6}{25}-\frac {11}{390625 (3+5 x)}+\frac {196 \log (3+5 x)}{390625}\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 59, normalized size = 0.95 \begin {gather*} \frac {7302662+53832870 x+145829250 x^2+137733750 x^3-114778125 x^4-377409375 x^5-318937500 x^6-94921875 x^7+980 (3+5 x) \log (3+5 x)}{1953125 (3+5 x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 47, normalized size = 0.76
method | result | size |
risch | \(-\frac {243 x^{6}}{25}-\frac {16767 x^{5}}{625}-\frac {14094 x^{4}}{625}+\frac {5553 x^{3}}{3125}+\frac {40743 x^{2}}{3125}+\frac {555489 x}{78125}-\frac {11}{1953125 \left (x +\frac {3}{5}\right )}+\frac {196 \ln \left (3+5 x \right )}{390625}\) | \(45\) |
default | \(\frac {555489 x}{78125}+\frac {40743 x^{2}}{3125}+\frac {5553 x^{3}}{3125}-\frac {14094 x^{4}}{625}-\frac {16767 x^{5}}{625}-\frac {243 x^{6}}{25}-\frac {11}{390625 \left (3+5 x \right )}+\frac {196 \ln \left (3+5 x \right )}{390625}\) | \(47\) |
norman | \(\frac {\frac {4999412}{234375} x +\frac {1166634}{15625} x^{2}+\frac {220374}{3125} x^{3}-\frac {36729}{625} x^{4}-\frac {120771}{625} x^{5}-\frac {20412}{125} x^{6}-\frac {243}{5} x^{7}}{3+5 x}+\frac {196 \ln \left (3+5 x \right )}{390625}\) | \(52\) |
meijerg | \(-\frac {1024 x}{45 \left (1+\frac {5 x}{3}\right )}+\frac {196 \ln \left (1+\frac {5 x}{3}\right )}{390625}+\frac {336 x \left (5 x +6\right )}{25 \left (1+\frac {5 x}{3}\right )}-\frac {2268 x \left (\frac {625}{27} x^{3}-\frac {250}{9} x^{2}+50 x +60\right )}{625 \left (1+\frac {5 x}{3}\right )}+\frac {15309 x \left (-\frac {625}{27} x^{4}+\frac {625}{27} x^{3}-\frac {250}{9} x^{2}+50 x +60\right )}{3125 \left (1+\frac {5 x}{3}\right )}-\frac {59049 x \left (\frac {43750}{243} x^{5}-\frac {4375}{27} x^{4}+\frac {4375}{27} x^{3}-\frac {1750}{9} x^{2}+350 x +420\right )}{156250 \left (1+\frac {5 x}{3}\right )}+\frac {59049 x \left (-\frac {312500}{729} x^{6}+\frac {87500}{243} x^{5}-\frac {8750}{27} x^{4}+\frac {8750}{27} x^{3}-\frac {3500}{9} x^{2}+700 x +840\right )}{1562500 \left (1+\frac {5 x}{3}\right )}\) | \(165\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 46, normalized size = 0.74 \begin {gather*} -\frac {243}{25} \, x^{6} - \frac {16767}{625} \, x^{5} - \frac {14094}{625} \, x^{4} + \frac {5553}{3125} \, x^{3} + \frac {40743}{3125} \, x^{2} + \frac {555489}{78125} \, x - \frac {11}{390625 \, {\left (5 \, x + 3\right )}} + \frac {196}{390625} \, \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 = 1.00, size = 57, normalized size = 0.92 \begin {gather*} -\frac {18984375 \, x^{7} + 63787500 \, x^{6} + 75481875 \, x^{5} + 22955625 \, x^{4} - 27546750 \, x^{3} - 29165850 \, x^{2} - 196 \, {\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 8332335 \, x + 11}{390625 \, {\left (5 \, x + 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 54, normalized size = 0.87 \begin {gather*} - \frac {243 x^{6}}{25} - \frac {16767 x^{5}}{625} - \frac {14094 x^{4}}{625} + \frac {5553 x^{3}}{3125} + \frac {40743 x^{2}}{3125} + \frac {555489 x}{78125} + \frac {196 \log {\left (5 x + 3 \right )}}{390625} - \frac {11}{1953125 x + 1171875} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.69, size = 84, normalized size = 1.35 \begin {gather*} \frac {9}{1953125} \, {\left (5 \, x + 3\right )}^{6} {\left (\frac {567}{5 \, x + 3} + \frac {1890}{{\left (5 \, x + 3\right )}^{2}} + \frac {2275}{{\left (5 \, x + 3\right )}^{3}} + \frac {1575}{{\left (5 \, x + 3\right )}^{4}} + \frac {805}{{\left (5 \, x + 3\right )}^{5}} - 135\right )} - \frac {11}{390625 \, {\left (5 \, x + 3\right )}} - \frac {196}{390625} \, \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 = 44, normalized size = 0.71 \begin {gather*} \frac {555489\,x}{78125}+\frac {196\,\ln \left (x+\frac {3}{5}\right )}{390625}-\frac {11}{1953125\,\left (x+\frac {3}{5}\right )}+\frac {40743\,x^2}{3125}+\frac {5553\,x^3}{3125}-\frac {14094\,x^4}{625}-\frac {16767\,x^5}{625}-\frac {243\,x^6}{25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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