Optimal. Leaf size=73 \[ \frac {424432 x}{390625}-\frac {62097 x^2}{31250}-\frac {393 x^3}{625}+\frac {22977 x^4}{6250}-\frac {324 x^5}{3125}-\frac {324 x^6}{125}-\frac {1331}{3906250 (3+5 x)^2}-\frac {19239}{1953125 (3+5 x)}+\frac {109032 \log (3+5 x)}{1953125} \]
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Rubi [A]
time = 0.02, 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 {324 x^6}{125}-\frac {324 x^5}{3125}+\frac {22977 x^4}{6250}-\frac {393 x^3}{625}-\frac {62097 x^2}{31250}+\frac {424432 x}{390625}-\frac {19239}{1953125 (5 x+3)}-\frac {1331}{3906250 (5 x+3)^2}+\frac {109032 \log (5 x+3)}{1953125} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {(1-2 x)^3 (2+3 x)^5}{(3+5 x)^3} \, dx &=\int \left (\frac {424432}{390625}-\frac {62097 x}{15625}-\frac {1179 x^2}{625}+\frac {45954 x^3}{3125}-\frac {324 x^4}{625}-\frac {1944 x^5}{125}+\frac {1331}{390625 (3+5 x)^3}+\frac {19239}{390625 (3+5 x)^2}+\frac {109032}{390625 (3+5 x)}\right ) \, dx\\ &=\frac {424432 x}{390625}-\frac {62097 x^2}{31250}-\frac {393 x^3}{625}+\frac {22977 x^4}{6250}-\frac {324 x^5}{3125}-\frac {324 x^6}{125}-\frac {1331}{3906250 (3+5 x)^2}-\frac {19239}{1953125 (3+5 x)}+\frac {109032 \log (3+5 x)}{1953125}\\ \end {align*}
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Mathematica [A]
time = 0.03, size = 68, normalized size = 0.93 \begin {gather*} \frac {151973789+698557830 x+711123525 x^2-744310000 x^3-692475000 x^4+1828837500 x^5+1278703125 x^6-1569375000 x^7-1265625000 x^8+1090320 (3+5 x)^2 \log (6 (3+5 x))}{19531250 (3+5 x)^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 56, normalized size = 0.77
method | result | size |
risch | \(-\frac {324 x^{6}}{125}-\frac {324 x^{5}}{3125}+\frac {22977 x^{4}}{6250}-\frac {393 x^{3}}{625}-\frac {62097 x^{2}}{31250}+\frac {424432 x}{390625}+\frac {-\frac {19239 x}{390625}-\frac {23353}{781250}}{\left (3+5 x \right )^{2}}+\frac {109032 \ln \left (3+5 x \right )}{1953125}\) | \(52\) |
default | \(\frac {424432 x}{390625}-\frac {62097 x^{2}}{31250}-\frac {393 x^{3}}{625}+\frac {22977 x^{4}}{6250}-\frac {324 x^{5}}{3125}-\frac {324 x^{6}}{125}-\frac {1331}{3906250 \left (3+5 x \right )^{2}}-\frac {19239}{1953125 \left (3+5 x \right )}+\frac {109032 \ln \left (3+5 x \right )}{1953125}\) | \(56\) |
norman | \(\frac {\frac {11518712}{1171875} x +\frac {10403068}{703125} x^{2}-\frac {595448}{15625} x^{3}-\frac {110796}{3125} x^{4}+\frac {292614}{3125} x^{5}+\frac {81837}{1250} x^{6}-\frac {10044}{125} x^{7}-\frac {324}{5} x^{8}}{\left (3+5 x \right )^{2}}+\frac {109032 \ln \left (3+5 x \right )}{1953125}\) | \(57\) |
meijerg | \(\frac {16 x \left (\frac {5 x}{3}+2\right )}{27 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {8 x^{2}}{9 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {56 x \left (15 x +6\right )}{75 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {109032 \ln \left (1+\frac {5 x}{3}\right )}{1953125}-\frac {154 x \left (\frac {100}{9} x^{2}+30 x +12\right )}{125 \left (1+\frac {5 x}{3}\right )^{2}}-\frac {63 x \left (-\frac {625}{27} x^{3}+\frac {500}{9} x^{2}+150 x +60\right )}{125 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {7749 x \left (\frac {1250}{81} x^{4}-\frac {625}{27} x^{3}+\frac {500}{9} x^{2}+150 x +60\right )}{6250 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {729 x \left (-\frac {21875}{243} x^{5}+\frac {8750}{81} x^{4}-\frac {4375}{27} x^{3}+\frac {3500}{9} x^{2}+1050 x +420\right )}{31250 \left (1+\frac {5 x}{3}\right )^{2}}-\frac {72171 x \left (\frac {125000}{729} x^{6}-\frac {43750}{243} x^{5}+\frac {17500}{81} x^{4}-\frac {8750}{27} x^{3}+\frac {7000}{9} x^{2}+2100 x +840\right )}{781250 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {26244 x \left (-\frac {390625}{729} x^{7}+\frac {125000}{243} x^{6}-\frac {43750}{81} x^{5}+\frac {17500}{27} x^{4}-\frac {8750}{9} x^{3}+\frac {7000}{3} x^{2}+6300 x +2520\right )}{1953125 \left (1+\frac {5 x}{3}\right )^{2}}\) | \(247\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 56, normalized size = 0.77 \begin {gather*} -\frac {324}{125} \, x^{6} - \frac {324}{3125} \, x^{5} + \frac {22977}{6250} \, x^{4} - \frac {393}{625} \, x^{3} - \frac {62097}{31250} \, x^{2} + \frac {424432}{390625} \, x - \frac {121 \, {\left (318 \, x + 193\right )}}{781250 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac {109032}{1953125} \, \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 = 72, normalized size = 0.99 \begin {gather*} -\frac {253125000 \, x^{8} + 313875000 \, x^{7} - 255740625 \, x^{6} - 365767500 \, x^{5} + 138495000 \, x^{4} + 148862000 \, x^{3} - 57470475 \, x^{2} - 218064 \, {\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 38006490 \, x + 116765}{3906250 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 63, normalized size = 0.86 \begin {gather*} - \frac {324 x^{6}}{125} - \frac {324 x^{5}}{3125} + \frac {22977 x^{4}}{6250} - \frac {393 x^{3}}{625} - \frac {62097 x^{2}}{31250} + \frac {424432 x}{390625} - \frac {38478 x + 23353}{19531250 x^{2} + 23437500 x + 7031250} + \frac {109032 \log {\left (5 x + 3 \right )}}{1953125} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.62, size = 52, normalized size = 0.71 \begin {gather*} -\frac {324}{125} \, x^{6} - \frac {324}{3125} \, x^{5} + \frac {22977}{6250} \, x^{4} - \frac {393}{625} \, x^{3} - \frac {62097}{31250} \, x^{2} + \frac {424432}{390625} \, x - \frac {121 \, {\left (318 \, x + 193\right )}}{781250 \, {\left (5 \, x + 3\right )}^{2}} + \frac {109032}{1953125} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 52, normalized size = 0.71 \begin {gather*} \frac {424432\,x}{390625}+\frac {109032\,\ln \left (x+\frac {3}{5}\right )}{1953125}-\frac {\frac {19239\,x}{9765625}+\frac {23353}{19531250}}{x^2+\frac {6\,x}{5}+\frac {9}{25}}-\frac {62097\,x^2}{31250}-\frac {393\,x^3}{625}+\frac {22977\,x^4}{6250}-\frac {324\,x^5}{3125}-\frac {324\,x^6}{125} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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