Optimal. Leaf size=69 \[ \frac {2187 x^4}{400}+\frac {16281 x^3}{500}+\frac {1974861 x^2}{20000}+\frac {6156243 x}{25000}+\frac {823543}{7744 (1-2 x)}-\frac {1}{1890625 (5 x+3)}+\frac {18941489 \log (1-2 x)}{85184}+\frac {47 \log (5 x+3)}{4159375} \]
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Rubi [A] time = 0.04, antiderivative size = 69, 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 = {88} \[ \frac {2187 x^4}{400}+\frac {16281 x^3}{500}+\frac {1974861 x^2}{20000}+\frac {6156243 x}{25000}+\frac {823543}{7744 (1-2 x)}-\frac {1}{1890625 (5 x+3)}+\frac {18941489 \log (1-2 x)}{85184}+\frac {47 \log (5 x+3)}{4159375} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(2+3 x)^7}{(1-2 x)^2 (3+5 x)^2} \, dx &=\int \left (\frac {6156243}{25000}+\frac {1974861 x}{10000}+\frac {48843 x^2}{500}+\frac {2187 x^3}{100}+\frac {823543}{3872 (-1+2 x)^2}+\frac {18941489}{42592 (-1+2 x)}+\frac {1}{378125 (3+5 x)^2}+\frac {47}{831875 (3+5 x)}\right ) \, dx\\ &=\frac {823543}{7744 (1-2 x)}+\frac {6156243 x}{25000}+\frac {1974861 x^2}{20000}+\frac {16281 x^3}{500}+\frac {2187 x^4}{400}-\frac {1}{1890625 (3+5 x)}+\frac {18941489 \log (1-2 x)}{85184}+\frac {47 \log (3+5 x)}{4159375}\\ \end {align*}
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Mathematica [A] time = 0.05, size = 74, normalized size = 1.07 \[ \frac {-\frac {11 (64339297003 x+38603578061)}{10 x^2+x-3}+89842500 (3 x+2)^4+886446000 (3 x+2)^3+7128103950 (3 x+2)^2+67228064640 (3 x+2)+295960765625 \log (3-6 x)+15040 \log (-3 (5 x+3))}{1331000000} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.64, size = 74, normalized size = 1.07 \[ \frac {72772425000 \, x^{6} + 440677462500 \, x^{5} + 1335778290000 \, x^{4} + 3278990706750 \, x^{3} - 66522621330 \, x^{2} + 15040 \, {\left (10 \, x^{2} + x - 3\right )} \log \left (5 \, x + 3\right ) + 295960765625 \, {\left (10 \, x^{2} + x - 3\right )} \log \left (2 \, x - 1\right ) - 1691007398993 \, x - 424639358671}{1331000000 \, {\left (10 \, x^{2} + x - 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.17, size = 103, normalized size = 1.49 \[ -\frac {{\left (5 \, x + 3\right )}^{4} {\left (\frac {142957386}{5 \, x + 3} + \frac {1626867990}{{\left (5 \, x + 3\right )}^{2}} + \frac {26903695995}{{\left (5 \, x + 3\right )}^{3}} - \frac {295961527385}{{\left (5 \, x + 3\right )}^{4}} + 11643588\right )}}{665500000 \, {\left (\frac {11}{5 \, x + 3} - 2\right )}} - \frac {1}{1890625 \, {\left (5 \, x + 3\right )}} - \frac {44471943}{200000} \, \log \left (\frac {{\left | 5 \, x + 3 \right |}}{5 \, {\left (5 \, x + 3\right )}^{2}}\right ) + \frac {18941489}{85184} \, \log \left ({\left | -\frac {11}{5 \, x + 3} + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 54, normalized size = 0.78 \[ \frac {2187 x^{4}}{400}+\frac {16281 x^{3}}{500}+\frac {1974861 x^{2}}{20000}+\frac {6156243 x}{25000}+\frac {18941489 \ln \left (2 x -1\right )}{85184}+\frac {47 \ln \left (5 x +3\right )}{4159375}-\frac {1}{1890625 \left (5 x +3\right )}-\frac {823543}{7744 \left (2 x -1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.59, size = 52, normalized size = 0.75 \[ \frac {2187}{400} \, x^{4} + \frac {16281}{500} \, x^{3} + \frac {1974861}{20000} \, x^{2} + \frac {6156243}{25000} \, x - \frac {64339297003 \, x + 38603578061}{121000000 \, {\left (10 \, x^{2} + x - 3\right )}} + \frac {47}{4159375} \, \log \left (5 \, x + 3\right ) + \frac {18941489}{85184} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 48, normalized size = 0.70 \[ \frac {6156243\,x}{25000}+\frac {18941489\,\ln \left (x-\frac {1}{2}\right )}{85184}+\frac {47\,\ln \left (x+\frac {3}{5}\right )}{4159375}-\frac {\frac {64339297003\,x}{1210000000}+\frac {38603578061}{1210000000}}{x^2+\frac {x}{10}-\frac {3}{10}}+\frac {1974861\,x^2}{20000}+\frac {16281\,x^3}{500}+\frac {2187\,x^4}{400} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.18, size = 61, normalized size = 0.88 \[ \frac {2187 x^{4}}{400} + \frac {16281 x^{3}}{500} + \frac {1974861 x^{2}}{20000} + \frac {6156243 x}{25000} + \frac {- 64339297003 x - 38603578061}{1210000000 x^{2} + 121000000 x - 363000000} + \frac {18941489 \log {\left (x - \frac {1}{2} \right )}}{85184} + \frac {47 \log {\left (x + \frac {3}{5} \right )}}{4159375} \]
Verification of antiderivative is not currently implemented for this CAS.
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