Optimal. Leaf size=20 \[ d x+\frac {e x^2}{2}+\frac {f x^3}{3} \]
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Rubi [A] time = 0.03, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 63, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.016, Rules used = {1586} \begin {gather*} d x+\frac {e x^2}{2}+\frac {f x^3}{3} \end {gather*}
Antiderivative was successfully verified.
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Rule 1586
Rubi steps
\begin {align*} \int \frac {a d+a e x+(b d+a f) x^2+b e x^3+(c d+b f) x^4+c e x^5+c f x^6}{a+b x^2+c x^4} \, dx &=\int \left (d+e x+f x^2\right ) \, dx\\ &=d x+\frac {e x^2}{2}+\frac {f x^3}{3}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 20, normalized size = 1.00 \begin {gather*} d x+\frac {e x^2}{2}+\frac {f x^3}{3} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 2.16, size = 19, normalized size = 0.95 \begin {gather*} \frac {1}{6} x \left (6 d+3 e x+2 f x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.88, size = 16, normalized size = 0.80 \begin {gather*} \frac {1}{3} \, f x^{3} + \frac {1}{2} \, e x^{2} + d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.77, size = 17, normalized size = 0.85 \begin {gather*} \frac {1}{3} \, f x^{3} + \frac {1}{2} \, x^{2} e + d 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}{3} f \,x^{3}+\frac {1}{2} e \,x^{2}+d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.62, size = 16, normalized size = 0.80 \begin {gather*} \frac {1}{3} \, f x^{3} + \frac {1}{2} \, e x^{2} + d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 16, normalized size = 0.80 \begin {gather*} \frac {f\,x^3}{3}+\frac {e\,x^2}{2}+d\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 15, normalized size = 0.75 \begin {gather*} d x + \frac {e x^{2}}{2} + \frac {f x^{3}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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