Optimal. Leaf size=23 \[ 3 x-\frac {7 x^2}{2}-\frac {8 x^3}{3}+5 x^4 \]
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Rubi [A]
time = 0.01, antiderivative size = 23, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {45}
\begin {gather*} 5 x^4-\frac {8 x^3}{3}-\frac {7 x^2}{2}+3 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) \, dx &=\int \left (3-7 x-8 x^2+20 x^3\right ) \, dx\\ &=3 x-\frac {7 x^2}{2}-\frac {8 x^3}{3}+5 x^4\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 23, normalized size = 1.00 \begin {gather*} 3 x-\frac {7 x^2}{2}-\frac {8 x^3}{3}+5 x^4 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 20, normalized size = 0.87
method | result | size |
gosper | \(\frac {x \left (30 x^{3}-16 x^{2}-21 x +18\right )}{6}\) | \(19\) |
default | \(3 x -\frac {7}{2} x^{2}-\frac {8}{3} x^{3}+5 x^{4}\) | \(20\) |
norman | \(3 x -\frac {7}{2} x^{2}-\frac {8}{3} x^{3}+5 x^{4}\) | \(20\) |
risch | \(3 x -\frac {7}{2} x^{2}-\frac {8}{3} x^{3}+5 x^{4}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 19, normalized size = 0.83 \begin {gather*} 5 \, x^{4} - \frac {8}{3} \, x^{3} - \frac {7}{2} \, x^{2} + 3 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.72, size = 19, normalized size = 0.83 \begin {gather*} 5 \, x^{4} - \frac {8}{3} \, x^{3} - \frac {7}{2} \, x^{2} + 3 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 20, normalized size = 0.87 \begin {gather*} 5 x^{4} - \frac {8 x^{3}}{3} - \frac {7 x^{2}}{2} + 3 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.96, size = 19, normalized size = 0.83 \begin {gather*} 5 \, x^{4} - \frac {8}{3} \, x^{3} - \frac {7}{2} \, x^{2} + 3 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 19, normalized size = 0.83 \begin {gather*} 5\,x^4-\frac {8\,x^3}{3}-\frac {7\,x^2}{2}+3\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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