Optimal. Leaf size=73 \[ \frac {486 x^6}{125}+\frac {17496 x^5}{3125}-\frac {23571 x^4}{12500}-\frac {16299 x^3}{3125}+\frac {189 x^2}{15625}+\frac {920502 x}{390625}-\frac {2134}{1953125 (5 x+3)}-\frac {121}{3906250 (5 x+3)^2}+\frac {15547 \log (5 x+3)}{1953125} \]
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Rubi [A] time = 0.04, 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 = {88} \[ \frac {486 x^6}{125}+\frac {17496 x^5}{3125}-\frac {23571 x^4}{12500}-\frac {16299 x^3}{3125}+\frac {189 x^2}{15625}+\frac {920502 x}{390625}-\frac {2134}{1953125 (5 x+3)}-\frac {121}{3906250 (5 x+3)^2}+\frac {15547 \log (5 x+3)}{1953125} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(1-2 x)^2 (2+3 x)^6}{(3+5 x)^3} \, dx &=\int \left (\frac {920502}{390625}+\frac {378 x}{15625}-\frac {48897 x^2}{3125}-\frac {23571 x^3}{3125}+\frac {17496 x^4}{625}+\frac {2916 x^5}{125}+\frac {121}{390625 (3+5 x)^3}+\frac {2134}{390625 (3+5 x)^2}+\frac {15547}{390625 (3+5 x)}\right ) \, dx\\ &=\frac {920502 x}{390625}+\frac {189 x^2}{15625}-\frac {16299 x^3}{3125}-\frac {23571 x^4}{12500}+\frac {17496 x^5}{3125}+\frac {486 x^6}{125}-\frac {121}{3906250 (3+5 x)^2}-\frac {2134}{1953125 (3+5 x)}+\frac {15547 \log (3+5 x)}{1953125}\\ \end {align*}
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Mathematica [A] time = 0.05, size = 68, normalized size = 0.93 \[ \frac {3796875000 x^8+10023750000 x^7+6086390625 x^6-5334918750 x^5-6763246875 x^4+481792500 x^3+3528738675 x^2+1743814610 x+310940 (5 x+3)^2 \log (6 (5 x+3))+274543613}{39062500 (5 x+3)^2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.46, size = 72, normalized size = 0.99 \[ \frac {759375000 \, x^{8} + 2004750000 \, x^{7} + 1217278125 \, x^{6} - 1066983750 \, x^{5} - 1352649375 \, x^{4} + 96358500 \, x^{3} + 553151700 \, x^{2} + 62188 \, {\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 165647680 \, x - 25850}{7812500 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.89, size = 52, normalized size = 0.71 \[ \frac {486}{125} \, x^{6} + \frac {17496}{3125} \, x^{5} - \frac {23571}{12500} \, x^{4} - \frac {16299}{3125} \, x^{3} + \frac {189}{15625} \, x^{2} + \frac {920502}{390625} \, x - \frac {11 \, {\left (388 \, x + 235\right )}}{781250 \, {\left (5 \, x + 3\right )}^{2}} + \frac {15547}{1953125} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 56, normalized size = 0.77 \[ \frac {486 x^{6}}{125}+\frac {17496 x^{5}}{3125}-\frac {23571 x^{4}}{12500}-\frac {16299 x^{3}}{3125}+\frac {189 x^{2}}{15625}+\frac {920502 x}{390625}+\frac {15547 \ln \left (5 x +3\right )}{1953125}-\frac {121}{3906250 \left (5 x +3\right )^{2}}-\frac {2134}{1953125 \left (5 x +3\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.51, size = 56, normalized size = 0.77 \[ \frac {486}{125} \, x^{6} + \frac {17496}{3125} \, x^{5} - \frac {23571}{12500} \, x^{4} - \frac {16299}{3125} \, x^{3} + \frac {189}{15625} \, x^{2} + \frac {920502}{390625} \, x - \frac {11 \, {\left (388 \, x + 235\right )}}{781250 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac {15547}{1953125} \, \log \left (5 \, x + 3\right ) \]
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 \[ \frac {920502\,x}{390625}+\frac {15547\,\ln \left (x+\frac {3}{5}\right )}{1953125}-\frac {\frac {2134\,x}{9765625}+\frac {517}{3906250}}{x^2+\frac {6\,x}{5}+\frac {9}{25}}+\frac {189\,x^2}{15625}-\frac {16299\,x^3}{3125}-\frac {23571\,x^4}{12500}+\frac {17496\,x^5}{3125}+\frac {486\,x^6}{125} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 65, normalized size = 0.89 \[ \frac {486 x^{6}}{125} + \frac {17496 x^{5}}{3125} - \frac {23571 x^{4}}{12500} - \frac {16299 x^{3}}{3125} + \frac {189 x^{2}}{15625} + \frac {920502 x}{390625} + \frac {- 4268 x - 2585}{19531250 x^{2} + 23437500 x + 7031250} + \frac {15547 \log {\left (5 x + 3 \right )}}{1953125} \]
Verification of antiderivative is not currently implemented for this CAS.
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