Optimal. Leaf size=16 \[ \frac {x}{a \sqrt [4]{a+b x^4}} \]
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Rubi [A] time = 0.00, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {191} \[ \frac {x}{a \sqrt [4]{a+b x^4}} \]
Antiderivative was successfully verified.
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Rule 191
Rubi steps
\begin {align*} \int \frac {1}{\left (a+b x^4\right )^{5/4}} \, dx &=\frac {x}{a \sqrt [4]{a+b x^4}}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 16, normalized size = 1.00 \[ \frac {x}{a \sqrt [4]{a+b x^4}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.82, size = 23, normalized size = 1.44 \[ \frac {{\left (b x^{4} + a\right )}^{\frac {3}{4}} x}{a b x^{4} + a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{{\left (b x^{4} + a\right )}^{\frac {5}{4}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 15, normalized size = 0.94 \[ \frac {x}{\left (b \,x^{4}+a \right )^{\frac {1}{4}} a} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.36, size = 14, normalized size = 0.88 \[ \frac {x}{{\left (b x^{4} + a\right )}^{\frac {1}{4}} a} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.02, size = 14, normalized size = 0.88 \[ \frac {x}{a\,{\left (b\,x^4+a\right )}^{1/4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 1.08, size = 29, normalized size = 1.81 \[ \frac {x \Gamma \left (\frac {1}{4}\right )}{4 a^{\frac {5}{4}} \sqrt [4]{1 + \frac {b x^{4}}{a}} \Gamma \left (\frac {5}{4}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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