Optimal. Leaf size=56 \[ -\frac {125 (3 x+2)^{12}}{1458}+\frac {1025 (3 x+2)^{11}}{2673}-\frac {37}{162} (3 x+2)^{10}+\frac {107 (3 x+2)^9}{2187}-\frac {7 (3 x+2)^8}{1944} \]
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Rubi [A] time = 0.03, antiderivative size = 56, 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} \[ -\frac {125 (3 x+2)^{12}}{1458}+\frac {1025 (3 x+2)^{11}}{2673}-\frac {37}{162} (3 x+2)^{10}+\frac {107 (3 x+2)^9}{2187}-\frac {7 (3 x+2)^8}{1944} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int (1-2 x) (2+3 x)^7 (3+5 x)^3 \, dx &=\int \left (-\frac {7}{81} (2+3 x)^7+\frac {107}{81} (2+3 x)^8-\frac {185}{27} (2+3 x)^9+\frac {1025}{81} (2+3 x)^{10}-\frac {250}{81} (2+3 x)^{11}\right ) \, dx\\ &=-\frac {7 (2+3 x)^8}{1944}+\frac {107 (2+3 x)^9}{2187}-\frac {37}{162} (2+3 x)^{10}+\frac {1025 (2+3 x)^{11}}{2673}-\frac {125 (2+3 x)^{12}}{1458}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 67, normalized size = 1.20 \[ -\frac {91125 x^{12}}{2}-\frac {3262275 x^{11}}{11}-\frac {1703673 x^{10}}{2}-1398447 x^9-\frac {11183805 x^8}{8}-788238 x^7-98966 x^6+219224 x^5+199012 x^4+88800 x^3+23328 x^2+3456 x \]
Antiderivative was successfully verified.
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fricas [A] time = 0.59, size = 59, normalized size = 1.05 \[ -\frac {91125}{2} x^{12} - \frac {3262275}{11} x^{11} - \frac {1703673}{2} x^{10} - 1398447 x^{9} - \frac {11183805}{8} x^{8} - 788238 x^{7} - 98966 x^{6} + 219224 x^{5} + 199012 x^{4} + 88800 x^{3} + 23328 x^{2} + 3456 x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.20, size = 59, normalized size = 1.05 \[ -\frac {91125}{2} \, x^{12} - \frac {3262275}{11} \, x^{11} - \frac {1703673}{2} \, x^{10} - 1398447 \, x^{9} - \frac {11183805}{8} \, x^{8} - 788238 \, x^{7} - 98966 \, x^{6} + 219224 \, x^{5} + 199012 \, x^{4} + 88800 \, x^{3} + 23328 \, x^{2} + 3456 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 60, normalized size = 1.07 \[ -\frac {91125}{2} x^{12}-\frac {3262275}{11} x^{11}-\frac {1703673}{2} x^{10}-1398447 x^{9}-\frac {11183805}{8} x^{8}-788238 x^{7}-98966 x^{6}+219224 x^{5}+199012 x^{4}+88800 x^{3}+23328 x^{2}+3456 x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.52, size = 59, normalized size = 1.05 \[ -\frac {91125}{2} \, x^{12} - \frac {3262275}{11} \, x^{11} - \frac {1703673}{2} \, x^{10} - 1398447 \, x^{9} - \frac {11183805}{8} \, x^{8} - 788238 \, x^{7} - 98966 \, x^{6} + 219224 \, x^{5} + 199012 \, x^{4} + 88800 \, x^{3} + 23328 \, x^{2} + 3456 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 59, normalized size = 1.05 \[ -\frac {91125\,x^{12}}{2}-\frac {3262275\,x^{11}}{11}-\frac {1703673\,x^{10}}{2}-1398447\,x^9-\frac {11183805\,x^8}{8}-788238\,x^7-98966\,x^6+219224\,x^5+199012\,x^4+88800\,x^3+23328\,x^2+3456\,x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 65, normalized size = 1.16 \[ - \frac {91125 x^{12}}{2} - \frac {3262275 x^{11}}{11} - \frac {1703673 x^{10}}{2} - 1398447 x^{9} - \frac {11183805 x^{8}}{8} - 788238 x^{7} - 98966 x^{6} + 219224 x^{5} + 199012 x^{4} + 88800 x^{3} + 23328 x^{2} + 3456 x \]
Verification of antiderivative is not currently implemented for this CAS.
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