Optimal. Leaf size=23 \[ 8 x+4 x^2-\frac {x^4}{4}+\frac {8 x^5}{5} \]
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Rubi [A]
time = 0.00, antiderivative size = 23, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 0, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \frac {8 x^5}{5}-\frac {x^4}{4}+4 x^2+8 x \end {gather*}
Antiderivative was successfully verified.
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Rubi steps
\begin {align*} \int \left (8+8 x-x^3+8 x^4\right ) \, dx &=8 x+4 x^2-\frac {x^4}{4}+\frac {8 x^5}{5}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 23, normalized size = 1.00 \begin {gather*} 8 x+4 x^2-\frac {x^4}{4}+\frac {8 x^5}{5} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 20, normalized size = 0.87
method | result | size |
gosper | \(8 x +4 x^{2}-\frac {1}{4} x^{4}+\frac {8}{5} x^{5}\) | \(20\) |
default | \(8 x +4 x^{2}-\frac {1}{4} x^{4}+\frac {8}{5} x^{5}\) | \(20\) |
norman | \(8 x +4 x^{2}-\frac {1}{4} x^{4}+\frac {8}{5} x^{5}\) | \(20\) |
risch | \(8 x +4 x^{2}-\frac {1}{4} x^{4}+\frac {8}{5} x^{5}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 19, normalized size = 0.83 \begin {gather*} \frac {8}{5} \, x^{5} - \frac {1}{4} \, x^{4} + 4 \, x^{2} + 8 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 19, normalized size = 0.83 \begin {gather*} \frac {8}{5} \, x^{5} - \frac {1}{4} \, x^{4} + 4 \, x^{2} + 8 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 19, normalized size = 0.83 \begin {gather*} \frac {8 x^{5}}{5} - \frac {x^{4}}{4} + 4 x^{2} + 8 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 3.74, size = 19, normalized size = 0.83 \begin {gather*} \frac {8}{5} \, x^{5} - \frac {1}{4} \, x^{4} + 4 \, x^{2} + 8 \, 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*} \frac {8\,x^5}{5}-\frac {x^4}{4}+4\,x^2+8\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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