Optimal. Leaf size=34 \[ -\frac {77}{32} (1-2 x)^4+\frac {17}{10} (1-2 x)^5-\frac {5}{16} (1-2 x)^6 \]
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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 = {78}
\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 78
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*} 6 x-\frac {17 x^2}{2}-9 x^3+\frac {45 x^4}{2}+\frac {28 x^5}{5}-20 x^6 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 30, normalized size = 0.88
method | result | size |
gosper | \(-\frac {x \left (200 x^{5}-56 x^{4}-225 x^{3}+90 x^{2}+85 x -60\right )}{10}\) | \(29\) |
default | \(-20 x^{6}+\frac {28}{5} x^{5}+\frac {45}{2} x^{4}-9 x^{3}-\frac {17}{2} x^{2}+6 x\) | \(30\) |
norman | \(-20 x^{6}+\frac {28}{5} x^{5}+\frac {45}{2} x^{4}-9 x^{3}-\frac {17}{2} x^{2}+6 x\) | \(30\) |
risch | \(-20 x^{6}+\frac {28}{5} x^{5}+\frac {45}{2} x^{4}-9 x^{3}-\frac {17}{2} x^{2}+6 x\) | \(30\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, 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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Fricas [A]
time = 0.40, 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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Sympy [A]
time = 0.01, 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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Giac [A]
time = 1.42, 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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