Optimal. Leaf size=20 \[ a x+\frac {b x^3}{3}+\frac {c x^5}{5} \]
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Rubi [A] time = 0.00, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} a x+\frac {b x^3}{3}+\frac {c x^5}{5} \end {gather*}
Antiderivative was successfully verified.
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Rubi steps
\begin {align*} \int \left (a+b x^2+c x^4\right ) \, dx &=a x+\frac {b x^3}{3}+\frac {c x^5}{5}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 20, normalized size = 1.00 \begin {gather*} a x+\frac {b x^3}{3}+\frac {c x^5}{5} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \left (a+b x^2+c x^4\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 2.47, size = 16, normalized size = 0.80 \begin {gather*} \frac {1}{5} x^{5} c + \frac {1}{3} x^{3} b + x a \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 16, normalized size = 0.80 \begin {gather*} \frac {1}{5} \, c x^{5} + \frac {1}{3} \, b x^{3} + a x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 17, normalized size = 0.85 \begin {gather*} \frac {1}{5} c \,x^{5}+\frac {1}{3} b \,x^{3}+a x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.35, size = 16, normalized size = 0.80 \begin {gather*} \frac {1}{5} \, c x^{5} + \frac {1}{3} \, b x^{3} + a x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 16, normalized size = 0.80 \begin {gather*} \frac {c\,x^5}{5}+\frac {b\,x^3}{3}+a\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 15, normalized size = 0.75 \begin {gather*} a x + \frac {b x^{3}}{3} + \frac {c x^{5}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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