Optimal. Leaf size=19 \[ -\frac {\left (a-b x^4\right )^{5/4}}{5 b} \]
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Rubi [A] time = 0.00, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {261} \[ -\frac {\left (a-b x^4\right )^{5/4}}{5 b} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin {align*} \int x^3 \sqrt [4]{a-b x^4} \, dx &=-\frac {\left (a-b x^4\right )^{5/4}}{5 b}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 19, normalized size = 1.00 \[ -\frac {\left (a-b x^4\right )^{5/4}}{5 b} \]
Antiderivative was successfully verified.
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fricas [A] time = 1.04, size = 24, normalized size = 1.26 \[ \frac {{\left (b x^{4} - a\right )} {\left (-b x^{4} + a\right )}^{\frac {1}{4}}}{5 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 15, normalized size = 0.79 \[ -\frac {{\left (-b x^{4} + a\right )}^{\frac {5}{4}}}{5 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 16, normalized size = 0.84 \[ -\frac {\left (-b \,x^{4}+a \right )^{\frac {5}{4}}}{5 b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.28, size = 15, normalized size = 0.79 \[ -\frac {{\left (-b x^{4} + a\right )}^{\frac {5}{4}}}{5 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.11, size = 15, normalized size = 0.79 \[ -\frac {{\left (a-b\,x^4\right )}^{5/4}}{5\,b} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.69, size = 39, normalized size = 2.05 \[ \begin {cases} - \frac {a \sqrt [4]{a - b x^{4}}}{5 b} + \frac {x^{4} \sqrt [4]{a - b x^{4}}}{5} & \text {for}\: b \neq 0 \\\frac {\sqrt [4]{a} x^{4}}{4} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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