Optimal. Leaf size=40 \[ 27 x-\frac {27 x^2}{2}-87 x^3+\frac {179 x^4}{4}+174 x^5-50 x^6-\frac {1000 x^7}{7} \]
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Rubi [A]
time = 0.01, antiderivative size = 40, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {45}
\begin {gather*} -\frac {1000 x^7}{7}-50 x^6+174 x^5+\frac {179 x^4}{4}-87 x^3-\frac {27 x^2}{2}+27 x \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rubi steps
\begin {align*} \int (1-2 x)^3 (3+5 x)^3 \, dx &=\int \left (27-27 x-261 x^2+179 x^3+870 x^4-300 x^5-1000 x^6\right ) \, dx\\ &=27 x-\frac {27 x^2}{2}-87 x^3+\frac {179 x^4}{4}+174 x^5-50 x^6-\frac {1000 x^7}{7}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 40, normalized size = 1.00 \begin {gather*} 27 x-\frac {27 x^2}{2}-87 x^3+\frac {179 x^4}{4}+174 x^5-50 x^6-\frac {1000 x^7}{7} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 35, normalized size = 0.88
method | result | size |
gosper | \(-\frac {x \left (4000 x^{6}+1400 x^{5}-4872 x^{4}-1253 x^{3}+2436 x^{2}+378 x -756\right )}{28}\) | \(34\) |
default | \(27 x -\frac {27}{2} x^{2}-87 x^{3}+\frac {179}{4} x^{4}+174 x^{5}-50 x^{6}-\frac {1000}{7} x^{7}\) | \(35\) |
norman | \(27 x -\frac {27}{2} x^{2}-87 x^{3}+\frac {179}{4} x^{4}+174 x^{5}-50 x^{6}-\frac {1000}{7} x^{7}\) | \(35\) |
risch | \(27 x -\frac {27}{2} x^{2}-87 x^{3}+\frac {179}{4} x^{4}+174 x^{5}-50 x^{6}-\frac {1000}{7} x^{7}\) | \(35\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 34, normalized size = 0.85 \begin {gather*} -\frac {1000}{7} \, x^{7} - 50 \, x^{6} + 174 \, x^{5} + \frac {179}{4} \, x^{4} - 87 \, x^{3} - \frac {27}{2} \, x^{2} + 27 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.47, size = 34, normalized size = 0.85 \begin {gather*} -\frac {1000}{7} \, x^{7} - 50 \, x^{6} + 174 \, x^{5} + \frac {179}{4} \, x^{4} - 87 \, x^{3} - \frac {27}{2} \, x^{2} + 27 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 37, normalized size = 0.92 \begin {gather*} - \frac {1000 x^{7}}{7} - 50 x^{6} + 174 x^{5} + \frac {179 x^{4}}{4} - 87 x^{3} - \frac {27 x^{2}}{2} + 27 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.86, size = 34, normalized size = 0.85 \begin {gather*} -\frac {1000}{7} \, x^{7} - 50 \, x^{6} + 174 \, x^{5} + \frac {179}{4} \, x^{4} - 87 \, x^{3} - \frac {27}{2} \, x^{2} + 27 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.02, size = 34, normalized size = 0.85 \begin {gather*} -\frac {1000\,x^7}{7}-50\,x^6+174\,x^5+\frac {179\,x^4}{4}-87\,x^3-\frac {27\,x^2}{2}+27\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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