Optimal. Leaf size=73 \[ \frac {823543}{42592 (1-2 x)}+\frac {1467477 x}{50000}+\frac {21141 x^2}{2500}+\frac {729 x^3}{500}-\frac {1}{3781250 (3+5 x)^2}-\frac {47}{4159375 (3+5 x)}+\frac {7411887 \log (1-2 x)}{234256}+\frac {4761 \log (3+5 x)}{45753125} \]
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Rubi [A]
time = 0.03, antiderivative size = 73, 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 {729 x^3}{500}+\frac {21141 x^2}{2500}+\frac {1467477 x}{50000}+\frac {823543}{42592 (1-2 x)}-\frac {47}{4159375 (5 x+3)}-\frac {1}{3781250 (5 x+3)^2}+\frac {7411887 \log (1-2 x)}{234256}+\frac {4761 \log (5 x+3)}{45753125} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {(2+3 x)^7}{(1-2 x)^2 (3+5 x)^3} \, dx &=\int \left (\frac {1467477}{50000}+\frac {21141 x}{1250}+\frac {2187 x^2}{500}+\frac {823543}{21296 (-1+2 x)^2}+\frac {7411887}{117128 (-1+2 x)}+\frac {1}{378125 (3+5 x)^3}+\frac {47}{831875 (3+5 x)^2}+\frac {4761}{9150625 (3+5 x)}\right ) \, dx\\ &=\frac {823543}{42592 (1-2 x)}+\frac {1467477 x}{50000}+\frac {21141 x^2}{2500}+\frac {729 x^3}{500}-\frac {1}{3781250 (3+5 x)^2}-\frac {47}{4159375 (3+5 x)}+\frac {7411887 \log (1-2 x)}{234256}+\frac {4761 \log (3+5 x)}{45753125}\\ \end {align*}
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Mathematica [A]
time = 0.03, size = 67, normalized size = 0.92 \begin {gather*} \frac {\frac {11 \left (-14162188399-426293494632 x-1002031406415 x^2+42644641050 x^3+1161933052500 x^4+315347175000 x^5+48514950000 x^6\right )}{(-1+2 x) (3+5 x)^2}+231621468750 \log (1-2 x)+761760 \log (6+10 x)}{7320500000} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 58, normalized size = 0.79
method | result | size |
risch | \(\frac {729 x^{3}}{500}+\frac {21141 x^{2}}{2500}+\frac {1467477 x}{50000}+\frac {-\frac {12867862383}{26620000} x^{2}-\frac {193017894561}{332750000} x -\frac {115810711639}{665500000}}{\left (-1+2 x \right ) \left (3+5 x \right )^{2}}+\frac {7411887 \ln \left (-1+2 x \right )}{234256}+\frac {4761 \ln \left (3+5 x \right )}{45753125}\) | \(57\) |
default | \(\frac {729 x^{3}}{500}+\frac {21141 x^{2}}{2500}+\frac {1467477 x}{50000}-\frac {823543}{42592 \left (-1+2 x \right )}+\frac {7411887 \ln \left (-1+2 x \right )}{234256}-\frac {1}{3781250 \left (3+5 x \right )^{2}}-\frac {47}{4159375 \left (3+5 x \right )}+\frac {4761 \ln \left (3+5 x \right )}{45753125}\) | \(58\) |
norman | \(\frac {-\frac {95139592517}{59895000} x^{2}-\frac {648615301}{11979000} x^{3}-\frac {12222317303}{19965000} x +\frac {349191}{200} x^{4}+\frac {9477}{20} x^{5}+\frac {729}{10} x^{6}}{\left (-1+2 x \right ) \left (3+5 x \right )^{2}}+\frac {7411887 \ln \left (-1+2 x \right )}{234256}+\frac {4761 \ln \left (3+5 x \right )}{45753125}\) | \(62\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.32, size = 59, normalized size = 0.81 \begin {gather*} \frac {729}{500} \, x^{3} + \frac {21141}{2500} \, x^{2} + \frac {1467477}{50000} \, x - \frac {321696559575 \, x^{2} + 386035789122 \, x + 115810711639}{665500000 \, {\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )}} + \frac {4761}{45753125} \, \log \left (5 \, x + 3\right ) + \frac {7411887}{234256} \, \log \left (2 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.52, size = 95, normalized size = 1.30 \begin {gather*} \frac {533664450000 \, x^{6} + 3468818925000 \, x^{5} + 12781263577500 \, x^{4} + 6680945249550 \, x^{3} - 6674047531965 \, x^{2} + 761760 \, {\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )} \log \left (5 \, x + 3\right ) + 231621468750 \, {\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )} \log \left (2 \, x - 1\right ) - 6180073448472 \, x - 1273917828029}{7320500000 \, {\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.09, size = 65, normalized size = 0.89 \begin {gather*} \frac {729 x^{3}}{500} + \frac {21141 x^{2}}{2500} + \frac {1467477 x}{50000} + \frac {- 321696559575 x^{2} - 386035789122 x - 115810711639}{33275000000 x^{3} + 23292500000 x^{2} - 7986000000 x - 5989500000} + \frac {7411887 \log {\left (x - \frac {1}{2} \right )}}{234256} + \frac {4761 \log {\left (x + \frac {3}{5} \right )}}{45753125} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.54, size = 103, normalized size = 1.41 \begin {gather*} \frac {{\left (2 \, x - 1\right )}^{3} {\left (\frac {25349061375}{2 \, x - 1} + \frac {234545525775}{{\left (2 \, x - 1\right )}^{2}} + \frac {720756547985}{{\left (2 \, x - 1\right )}^{3}} + \frac {689127341628}{{\left (2 \, x - 1\right )}^{4}} + 1334161125\right )}}{292820000 \, {\left (\frac {11}{2 \, x - 1} + 5\right )}^{2}} - \frac {823543}{42592 \, {\left (2 \, x - 1\right )}} - \frac {1582011}{50000} \, \log \left (\frac {{\left | 2 \, x - 1 \right |}}{2 \, {\left (2 \, x - 1\right )}^{2}}\right ) + \frac {4761}{45753125} \, \log \left ({\left | -\frac {11}{2 \, x - 1} - 5 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 54, normalized size = 0.74 \begin {gather*} \frac {1467477\,x}{50000}+\frac {7411887\,\ln \left (x-\frac {1}{2}\right )}{234256}+\frac {4761\,\ln \left (x+\frac {3}{5}\right )}{45753125}+\frac {\frac {12867862383\,x^2}{1331000000}+\frac {193017894561\,x}{16637500000}+\frac {115810711639}{33275000000}}{-x^3-\frac {7\,x^2}{10}+\frac {6\,x}{25}+\frac {9}{50}}+\frac {21141\,x^2}{2500}+\frac {729\,x^3}{500} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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