Optimal. Leaf size=17 \[ \frac {a x^4}{4}+\frac {b x^8}{8} \]
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Rubi [A] time = 0.00, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {14} \[ \frac {a x^4}{4}+\frac {b x^8}{8} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int x^3 \left (a+b x^4\right ) \, dx &=\int \left (a x^3+b x^7\right ) \, dx\\ &=\frac {a x^4}{4}+\frac {b x^8}{8}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 17, normalized size = 1.00 \[ \frac {a x^4}{4}+\frac {b x^8}{8} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.63, size = 13, normalized size = 0.76 \[ \frac {1}{8} x^{8} b + \frac {1}{4} x^{4} a \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 13, normalized size = 0.76 \[ \frac {1}{8} \, b x^{8} + \frac {1}{4} \, a x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 14, normalized size = 0.82 \[ \frac {1}{8} b \,x^{8}+\frac {1}{4} a \,x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.29, size = 14, normalized size = 0.82 \[ \frac {{\left (b x^{4} + a\right )}^{2}}{8 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 13, normalized size = 0.76 \[ \frac {b\,x^8}{8}+\frac {a\,x^4}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.18, size = 12, normalized size = 0.71 \[ \frac {a x^{4}}{4} + \frac {b x^{8}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
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