Optimal. Leaf size=15 \[ \frac {\sqrt [4]{a+b x^4}}{b} \]
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Rubi [A]
time = 0.00, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {267}
\begin {gather*} \frac {\sqrt [4]{a+b x^4}}{b} \end {gather*}
Antiderivative was successfully verified.
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Rule 267
Rubi steps
\begin {align*} \int \frac {x^3}{\left (a+b x^4\right )^{3/4}} \, dx &=\frac {\sqrt [4]{a+b x^4}}{b}\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 15, normalized size = 1.00 \begin {gather*} \frac {\sqrt [4]{a+b x^4}}{b} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.15, size = 14, normalized size = 0.93
method | result | size |
gosper | \(\frac {\left (b \,x^{4}+a \right )^{\frac {1}{4}}}{b}\) | \(14\) |
derivativedivides | \(\frac {\left (b \,x^{4}+a \right )^{\frac {1}{4}}}{b}\) | \(14\) |
default | \(\frac {\left (b \,x^{4}+a \right )^{\frac {1}{4}}}{b}\) | \(14\) |
trager | \(\frac {\left (b \,x^{4}+a \right )^{\frac {1}{4}}}{b}\) | \(14\) |
risch | \(\frac {\left (b \,x^{4}+a \right )^{\frac {1}{4}}}{b}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 13, normalized size = 0.87 \begin {gather*} \frac {{\left (b x^{4} + a\right )}^{\frac {1}{4}}}{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 = 0.87 \begin {gather*} \frac {{\left (b x^{4} + a\right )}^{\frac {1}{4}}}{b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.20, size = 20, normalized size = 1.33 \begin {gather*} \begin {cases} \frac {\sqrt [4]{a + b x^{4}}}{b} & \text {for}\: b \neq 0 \\\frac {x^{4}}{4 a^{\frac {3}{4}}} & \text {otherwise} \end {cases} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.12, size = 13, normalized size = 0.87 \begin {gather*} \frac {{\left (b x^{4} + a\right )}^{\frac {1}{4}}}{b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.12, size = 13, normalized size = 0.87 \begin {gather*} \frac {{\left (b\,x^4+a\right )}^{1/4}}{b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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