Optimal. Leaf size=56 \[ -\frac {250 (3 x+2)^{11}}{2673}+\frac {205}{486} (3 x+2)^{10}-\frac {185}{729} (3 x+2)^9+\frac {107 (3 x+2)^8}{1944}-\frac {1}{243} (3 x+2)^7 \]
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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} \begin {gather*} -\frac {250 (3 x+2)^{11}}{2673}+\frac {205}{486} (3 x+2)^{10}-\frac {185}{729} (3 x+2)^9+\frac {107 (3 x+2)^8}{1944}-\frac {1}{243} (3 x+2)^7 \end {gather*}
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int (1-2 x) (2+3 x)^6 (3+5 x)^3 \, dx &=\int \left (-\frac {7}{81} (2+3 x)^6+\frac {107}{81} (2+3 x)^7-\frac {185}{27} (2+3 x)^8+\frac {1025}{81} (2+3 x)^9-\frac {250}{81} (2+3 x)^{10}\right ) \, dx\\ &=-\frac {1}{243} (2+3 x)^7+\frac {107 (2+3 x)^8}{1944}-\frac {185}{729} (2+3 x)^9+\frac {205}{486} (2+3 x)^{10}-\frac {250 (2+3 x)^{11}}{2673}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 60, normalized size = 1.07 \begin {gather*} -\frac {182250 x^{11}}{11}-\frac {193185 x^{10}}{2}-243945 x^9-\frac {2731671 x^8}{8}-272403 x^7-94668 x^6+36148 x^5+61220 x^4+34032 x^3+10368 x^2+1728 x \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int (1-2 x) (2+3 x)^6 (3+5 x)^3 \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.23, size = 54, normalized size = 0.96 \begin {gather*} -\frac {182250}{11} x^{11} - \frac {193185}{2} x^{10} - 243945 x^{9} - \frac {2731671}{8} x^{8} - 272403 x^{7} - 94668 x^{6} + 36148 x^{5} + 61220 x^{4} + 34032 x^{3} + 10368 x^{2} + 1728 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.28, size = 54, normalized size = 0.96 \begin {gather*} -\frac {182250}{11} \, x^{11} - \frac {193185}{2} \, x^{10} - 243945 \, x^{9} - \frac {2731671}{8} \, x^{8} - 272403 \, x^{7} - 94668 \, x^{6} + 36148 \, x^{5} + 61220 \, x^{4} + 34032 \, x^{3} + 10368 \, x^{2} + 1728 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 55, normalized size = 0.98 \begin {gather*} -\frac {182250}{11} x^{11}-\frac {193185}{2} x^{10}-243945 x^{9}-\frac {2731671}{8} x^{8}-272403 x^{7}-94668 x^{6}+36148 x^{5}+61220 x^{4}+34032 x^{3}+10368 x^{2}+1728 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.46, size = 54, normalized size = 0.96 \begin {gather*} -\frac {182250}{11} \, x^{11} - \frac {193185}{2} \, x^{10} - 243945 \, x^{9} - \frac {2731671}{8} \, x^{8} - 272403 \, x^{7} - 94668 \, x^{6} + 36148 \, x^{5} + 61220 \, x^{4} + 34032 \, x^{3} + 10368 \, x^{2} + 1728 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 54, normalized size = 0.96 \begin {gather*} -\frac {182250\,x^{11}}{11}-\frac {193185\,x^{10}}{2}-243945\,x^9-\frac {2731671\,x^8}{8}-272403\,x^7-94668\,x^6+36148\,x^5+61220\,x^4+34032\,x^3+10368\,x^2+1728\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 58, normalized size = 1.04 \begin {gather*} - \frac {182250 x^{11}}{11} - \frac {193185 x^{10}}{2} - 243945 x^{9} - \frac {2731671 x^{8}}{8} - 272403 x^{7} - 94668 x^{6} + 36148 x^{5} + 61220 x^{4} + 34032 x^{3} + 10368 x^{2} + 1728 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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