Optimal. Leaf size=26 \[ a x+4 x^2-\frac {8 x^3}{3}+x^4-\frac {x^5}{5} \]
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Rubi [A]
time = 0.00, antiderivative size = 26, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 0, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} a x-\frac {x^5}{5}+x^4-\frac {8 x^3}{3}+4 x^2 \end {gather*}
Antiderivative was successfully verified.
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Rubi steps
\begin {align*} \int \left (a+8 x-8 x^2+4 x^3-x^4\right ) \, dx &=a x+4 x^2-\frac {8 x^3}{3}+x^4-\frac {x^5}{5}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 26, normalized size = 1.00 \begin {gather*} a x+4 x^2-\frac {8 x^3}{3}+x^4-\frac {x^5}{5} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 23, normalized size = 0.88
method | result | size |
gosper | \(a x +4 x^{2}-\frac {8}{3} x^{3}+x^{4}-\frac {1}{5} x^{5}\) | \(23\) |
default | \(a x +4 x^{2}-\frac {8}{3} x^{3}+x^{4}-\frac {1}{5} x^{5}\) | \(23\) |
norman | \(a x +4 x^{2}-\frac {8}{3} x^{3}+x^{4}-\frac {1}{5} x^{5}\) | \(23\) |
risch | \(a x +4 x^{2}-\frac {8}{3} x^{3}+x^{4}-\frac {1}{5} x^{5}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 22, normalized size = 0.85 \begin {gather*} -\frac {1}{5} \, x^{5} + x^{4} - \frac {8}{3} \, x^{3} + a x + 4 \, x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 22, normalized size = 0.85 \begin {gather*} -\frac {1}{5} \, x^{5} + x^{4} - \frac {8}{3} \, x^{3} + a x + 4 \, x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 22, normalized size = 0.85 \begin {gather*} a x - \frac {x^{5}}{5} + x^{4} - \frac {8 x^{3}}{3} + 4 x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 4.93, size = 22, normalized size = 0.85 \begin {gather*} -\frac {1}{5} \, x^{5} + x^{4} - \frac {8}{3} \, x^{3} + a x + 4 \, x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.02, size = 22, normalized size = 0.85 \begin {gather*} -\frac {x^5}{5}+x^4-\frac {8\,x^3}{3}+4\,x^2+a\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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