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}
\begin {gather*} \frac {a x^4}{4}+\frac {b x^8}{8} \end {gather*}
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 \begin {gather*} \frac {a x^4}{4}+\frac {b x^8}{8} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.04, size = 15, normalized size = 0.88
method | result | size |
gosper | \(\frac {1}{4} a \,x^{4}+\frac {1}{8} b \,x^{8}\) | \(14\) |
norman | \(\frac {1}{4} a \,x^{4}+\frac {1}{8} b \,x^{8}\) | \(14\) |
default | \(\frac {\left (b \,x^{4}+a \right )^{2}}{8 b}\) | \(15\) |
risch | \(\frac {b \,x^{8}}{8}+\frac {a \,x^{4}}{4}+\frac {a^{2}}{8 b}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 14, normalized size = 0.82 \begin {gather*} \frac {{\left (b x^{4} + a\right )}^{2}}{8 \, b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 13, normalized size = 0.76 \begin {gather*} \frac {1}{8} \, b x^{8} + \frac {1}{4} \, a x^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 12, normalized size = 0.71 \begin {gather*} \frac {a x^{4}}{4} + \frac {b x^{8}}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 2.03, size = 13, normalized size = 0.76 \begin {gather*} \frac {1}{8} \, b x^{8} + \frac {1}{4} \, a x^{4} \end {gather*}
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 \begin {gather*} \frac {b\,x^8}{8}+\frac {a\,x^4}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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