Optimal. Leaf size=21 \[ \frac {4 x^5}{5}+\frac {4 x^3}{3}+2 x^2+x \]
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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 = {} \[ \frac {4 x^5}{5}+\frac {4 x^3}{3}+2 x^2+x \]
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 \[ \frac {4 x^5}{5}+\frac {4 x^3}{3}+2 x^2+x \]
Antiderivative was successfully verified.
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fricas [A] time = 0.34, size = 17, normalized size = 0.81 \[ \frac {4}{5} x^{5} + \frac {4}{3} x^{3} + 2 x^{2} + x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.36, size = 17, normalized size = 0.81 \[ \frac {4}{5} \, x^{5} + \frac {4}{3} \, x^{3} + 2 \, x^{2} + x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 18, normalized size = 0.86 \[ \frac {4}{5} x^{5}+\frac {4}{3} x^{3}+2 x^{2}+x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.57, size = 17, normalized size = 0.81 \[ \frac {4}{5} \, x^{5} + \frac {4}{3} \, x^{3} + 2 \, x^{2} + x \]
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 \[ \frac {4\,x^5}{5}+\frac {4\,x^3}{3}+2\,x^2+x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 19, normalized size = 0.90 \[ \frac {4 x^{5}}{5} + \frac {4 x^{3}}{3} + 2 x^{2} + x \]
Verification of antiderivative is not currently implemented for this CAS.
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