Optimal. Leaf size=34 \[ -\frac {5}{16} (1-2 x)^6+\frac {17}{10} (1-2 x)^5-\frac {77}{32} (1-2 x)^4 \]
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Rubi [A] time = 0.01, antiderivative size = 34, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {77} \begin {gather*} -\frac {5}{16} (1-2 x)^6+\frac {17}{10} (1-2 x)^5-\frac {77}{32} (1-2 x)^4 \end {gather*}
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int (1-2 x)^3 (2+3 x) (3+5 x) \, dx &=\int \left (\frac {77}{4} (1-2 x)^3-17 (1-2 x)^4+\frac {15}{4} (1-2 x)^5\right ) \, dx\\ &=-\frac {77}{32} (1-2 x)^4+\frac {17}{10} (1-2 x)^5-\frac {5}{16} (1-2 x)^6\\ \end {align*}
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Mathematica [A] time = 0.00, size = 35, normalized size = 1.03 \begin {gather*} -20 x^6+\frac {28 x^5}{5}+\frac {45 x^4}{2}-9 x^3-\frac {17 x^2}{2}+6 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)^3 (2+3 x) (3+5 x) \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.11, size = 29, normalized size = 0.85 \begin {gather*} -20 x^{6} + \frac {28}{5} x^{5} + \frac {45}{2} x^{4} - 9 x^{3} - \frac {17}{2} x^{2} + 6 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.90, size = 29, normalized size = 0.85 \begin {gather*} -20 \, x^{6} + \frac {28}{5} \, x^{5} + \frac {45}{2} \, x^{4} - 9 \, x^{3} - \frac {17}{2} \, x^{2} + 6 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 30, normalized size = 0.88 \begin {gather*} -20 x^{6}+\frac {28}{5} x^{5}+\frac {45}{2} x^{4}-9 x^{3}-\frac {17}{2} x^{2}+6 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.63, size = 29, normalized size = 0.85 \begin {gather*} -20 \, x^{6} + \frac {28}{5} \, x^{5} + \frac {45}{2} \, x^{4} - 9 \, x^{3} - \frac {17}{2} \, x^{2} + 6 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 29, normalized size = 0.85 \begin {gather*} -20\,x^6+\frac {28\,x^5}{5}+\frac {45\,x^4}{2}-9\,x^3-\frac {17\,x^2}{2}+6\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 32, normalized size = 0.94 \begin {gather*} - 20 x^{6} + \frac {28 x^{5}}{5} + \frac {45 x^{4}}{2} - 9 x^{3} - \frac {17 x^{2}}{2} + 6 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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