Optimal. Leaf size=21 \[ x+2 x^2+\frac {4 x^3}{3}+\frac {4 x^5}{5} \]
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Rubi [A]
time = 0.00, antiderivative size = 21, 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 {4 x^5}{5}+\frac {4 x^3}{3}+2 x^2+x \end {gather*}
Antiderivative was successfully verified.
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Rubi steps
\begin {align*} \int \left (1+4 x+4 x^2+4 x^4\right ) \, dx &=x+2 x^2+\frac {4 x^3}{3}+\frac {4 x^5}{5}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 21, normalized size = 1.00 \begin {gather*} x+2 x^2+\frac {4 x^3}{3}+\frac {4 x^5}{5} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 18, normalized size = 0.86
method | result | size |
gosper | \(x +2 x^{2}+\frac {4}{3} x^{3}+\frac {4}{5} x^{5}\) | \(18\) |
default | \(x +2 x^{2}+\frac {4}{3} x^{3}+\frac {4}{5} x^{5}\) | \(18\) |
norman | \(x +2 x^{2}+\frac {4}{3} x^{3}+\frac {4}{5} x^{5}\) | \(18\) |
risch | \(x +2 x^{2}+\frac {4}{3} x^{3}+\frac {4}{5} x^{5}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 17, normalized size = 0.81 \begin {gather*} \frac {4}{5} \, x^{5} + \frac {4}{3} \, x^{3} + 2 \, x^{2} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 17, normalized size = 0.81 \begin {gather*} \frac {4}{5} \, x^{5} + \frac {4}{3} \, x^{3} + 2 \, x^{2} + 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 = 0.90 \begin {gather*} \frac {4 x^{5}}{5} + \frac {4 x^{3}}{3} + 2 x^{2} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 3.47, size = 17, normalized size = 0.81 \begin {gather*} \frac {4}{5} \, x^{5} + \frac {4}{3} \, x^{3} + 2 \, x^{2} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 17, normalized size = 0.81 \begin {gather*} \frac {4\,x^5}{5}+\frac {4\,x^3}{3}+2\,x^2+x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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