Optimal. Leaf size=73 \[ \frac {7 (3 x+2)^{m+1}}{81 (m+1)}-\frac {8 (3 x+2)^{m+2}}{9 (m+2)}+\frac {65 (3 x+2)^{m+3}}{27 (m+3)}-\frac {50 (3 x+2)^{m+4}}{81 (m+4)} \]
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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 = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {77} \[ \frac {7 (3 x+2)^{m+1}}{81 (m+1)}-\frac {8 (3 x+2)^{m+2}}{9 (m+2)}+\frac {65 (3 x+2)^{m+3}}{27 (m+3)}-\frac {50 (3 x+2)^{m+4}}{81 (m+4)} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int (1-2 x) (2+3 x)^m (3+5 x)^2 \, dx &=\int \left (\frac {7}{27} (2+3 x)^m-\frac {8}{3} (2+3 x)^{1+m}+\frac {65}{9} (2+3 x)^{2+m}-\frac {50}{27} (2+3 x)^{3+m}\right ) \, dx\\ &=\frac {7 (2+3 x)^{1+m}}{81 (1+m)}-\frac {8 (2+3 x)^{2+m}}{9 (2+m)}+\frac {65 (2+3 x)^{3+m}}{27 (3+m)}-\frac {50 (2+3 x)^{4+m}}{81 (4+m)}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 61, normalized size = 0.84 \[ \frac {1}{81} (3 x+2)^{m+1} \left (-\frac {50 (3 x+2)^3}{m+4}+\frac {195 (3 x+2)^2}{m+3}-\frac {72 (3 x+2)}{m+2}+\frac {7}{m+1}\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.82, size = 120, normalized size = 1.64 \[ -\frac {{\left (1350 \, {\left (m^{3} + 6 \, m^{2} + 11 \, m + 6\right )} x^{4} + 45 \, {\left (41 \, m^{3} + 207 \, m^{2} + 334 \, m + 168\right )} x^{3} - 162 \, m^{3} + 18 \, {\left (17 \, m^{3} - 69 \, m^{2} - 302 \, m - 216\right )} x^{2} - 1314 \, m^{2} - 3 \, {\left (153 \, m^{3} + 1513 \, m^{2} + 3290 \, m + 1944\right )} x - 2644 \, m - 1520\right )} {\left (3 \, x + 2\right )}^{m}}{27 \, {\left (m^{4} + 10 \, m^{3} + 35 \, m^{2} + 50 \, m + 24\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.95, size = 278, normalized size = 3.81 \[ -\frac {1350 \, m^{3} {\left (3 \, x + 2\right )}^{m} x^{4} + 1845 \, m^{3} {\left (3 \, x + 2\right )}^{m} x^{3} + 8100 \, m^{2} {\left (3 \, x + 2\right )}^{m} x^{4} + 306 \, m^{3} {\left (3 \, x + 2\right )}^{m} x^{2} + 9315 \, m^{2} {\left (3 \, x + 2\right )}^{m} x^{3} + 14850 \, m {\left (3 \, x + 2\right )}^{m} x^{4} - 459 \, m^{3} {\left (3 \, x + 2\right )}^{m} x - 1242 \, m^{2} {\left (3 \, x + 2\right )}^{m} x^{2} + 15030 \, m {\left (3 \, x + 2\right )}^{m} x^{3} + 8100 \, {\left (3 \, x + 2\right )}^{m} x^{4} - 162 \, m^{3} {\left (3 \, x + 2\right )}^{m} - 4539 \, m^{2} {\left (3 \, x + 2\right )}^{m} x - 5436 \, m {\left (3 \, x + 2\right )}^{m} x^{2} + 7560 \, {\left (3 \, x + 2\right )}^{m} x^{3} - 1314 \, m^{2} {\left (3 \, x + 2\right )}^{m} - 9870 \, m {\left (3 \, x + 2\right )}^{m} x - 3888 \, {\left (3 \, x + 2\right )}^{m} x^{2} - 2644 \, m {\left (3 \, x + 2\right )}^{m} - 5832 \, {\left (3 \, x + 2\right )}^{m} x - 1520 \, {\left (3 \, x + 2\right )}^{m}}{27 \, {\left (m^{4} + 10 \, m^{3} + 35 \, m^{2} + 50 \, m + 24\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 120, normalized size = 1.64 \[ -\frac {\left (450 m^{3} x^{3}+315 m^{3} x^{2}+2700 m^{2} x^{3}-108 m^{3} x +1305 m^{2} x^{2}+4950 m \,x^{3}-81 m^{3}-1284 m^{2} x +1710 m \,x^{2}+2700 x^{3}-657 m^{2}-2952 m x +720 x^{2}-1322 m -1776 x -760\right ) \left (3 x +2\right )^{m +1}}{27 \left (m^{4}+10 m^{3}+35 m^{2}+50 m +24\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.47, size = 183, normalized size = 2.51 \[ -\frac {50 \, {\left (27 \, {\left (m^{3} + 6 \, m^{2} + 11 \, m + 6\right )} x^{4} + 18 \, {\left (m^{3} + 3 \, m^{2} + 2 \, m\right )} x^{3} - 36 \, {\left (m^{2} + m\right )} x^{2} + 48 \, m x - 32\right )} {\left (3 \, x + 2\right )}^{m}}{27 \, {\left (m^{4} + 10 \, m^{3} + 35 \, m^{2} + 50 \, m + 24\right )}} - \frac {35 \, {\left (27 \, {\left (m^{2} + 3 \, m + 2\right )} x^{3} + 18 \, {\left (m^{2} + m\right )} x^{2} - 24 \, m x + 16\right )} {\left (3 \, x + 2\right )}^{m}}{27 \, {\left (m^{3} + 6 \, m^{2} + 11 \, m + 6\right )}} + \frac {4 \, {\left (9 \, {\left (m + 1\right )} x^{2} + 6 \, m x - 4\right )} {\left (3 \, x + 2\right )}^{m}}{3 \, {\left (m^{2} + 3 \, m + 2\right )}} + \frac {3 \, {\left (3 \, x + 2\right )}^{m + 1}}{m + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.54, size = 211, normalized size = 2.89 \[ {\left (3\,x+2\right )}^m\,\left (\frac {162\,m^3+1314\,m^2+2644\,m+1520}{27\,m^4+270\,m^3+945\,m^2+1350\,m+648}+\frac {x\,\left (459\,m^3+4539\,m^2+9870\,m+5832\right )}{27\,m^4+270\,m^3+945\,m^2+1350\,m+648}+\frac {x^2\,\left (-306\,m^3+1242\,m^2+5436\,m+3888\right )}{27\,m^4+270\,m^3+945\,m^2+1350\,m+648}-\frac {x^4\,\left (1350\,m^3+8100\,m^2+14850\,m+8100\right )}{27\,m^4+270\,m^3+945\,m^2+1350\,m+648}-\frac {x^3\,\left (1845\,m^3+9315\,m^2+15030\,m+7560\right )}{27\,m^4+270\,m^3+945\,m^2+1350\,m+648}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.76, size = 1017, normalized size = 13.93 \[ \text {result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
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