Optimal. Leaf size=26 \[ 9 x-3 x^2-\frac {59 x^3}{3}+5 x^4+20 x^5 \]
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Rubi [A]
time = 0.01, antiderivative size = 26, 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*} 20 x^5+5 x^4-\frac {59 x^3}{3}-3 x^2+9 x \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rubi steps
\begin {align*} \int (1-2 x)^2 (3+5 x)^2 \, dx &=\int \left (9-6 x-59 x^2+20 x^3+100 x^4\right ) \, dx\\ &=9 x-3 x^2-\frac {59 x^3}{3}+5 x^4+20 x^5\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 26, normalized size = 1.00 \begin {gather*} 9 x-3 x^2-\frac {59 x^3}{3}+5 x^4+20 x^5 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 25, normalized size = 0.96
method | result | size |
gosper | \(\frac {x \left (60 x^{4}+15 x^{3}-59 x^{2}-9 x +27\right )}{3}\) | \(24\) |
default | \(9 x -3 x^{2}-\frac {59}{3} x^{3}+5 x^{4}+20 x^{5}\) | \(25\) |
norman | \(9 x -3 x^{2}-\frac {59}{3} x^{3}+5 x^{4}+20 x^{5}\) | \(25\) |
risch | \(9 x -3 x^{2}-\frac {59}{3} x^{3}+5 x^{4}+20 x^{5}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.39, size = 24, normalized size = 0.92 \begin {gather*} 20 \, x^{5} + 5 \, x^{4} - \frac {59}{3} \, x^{3} - 3 \, x^{2} + 9 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.41, size = 24, normalized size = 0.92 \begin {gather*} 20 \, x^{5} + 5 \, x^{4} - \frac {59}{3} \, x^{3} - 3 \, x^{2} + 9 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 24, normalized size = 0.92 \begin {gather*} 20 x^{5} + 5 x^{4} - \frac {59 x^{3}}{3} - 3 x^{2} + 9 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.58, size = 24, normalized size = 0.92 \begin {gather*} 20 \, x^{5} + 5 \, x^{4} - \frac {59}{3} \, x^{3} - 3 \, x^{2} + 9 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.02, size = 24, normalized size = 0.92 \begin {gather*} 20\,x^5+5\,x^4-\frac {59\,x^3}{3}-3\,x^2+9\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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