Optimal. Leaf size=21 \[ -\frac{\left (a+b x^4\right )^{3/4}}{3 a x^3} \]
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Rubi [A] time = 0.0047528, antiderivative size = 21, normalized size of antiderivative = 1., 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 = {264} \[ -\frac{\left (a+b x^4\right )^{3/4}}{3 a x^3} \]
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin{align*} \int \frac{1}{x^4 \sqrt [4]{a+b x^4}} \, dx &=-\frac{\left (a+b x^4\right )^{3/4}}{3 a x^3}\\ \end{align*}
Mathematica [A] time = 0.0043928, size = 21, normalized size = 1. \[ -\frac{\left (a+b x^4\right )^{3/4}}{3 a x^3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 18, normalized size = 0.9 \begin{align*} -{\frac{1}{3\,a{x}^{3}} \left ( b{x}^{4}+a \right ) ^{{\frac{3}{4}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.991343, size = 23, normalized size = 1.1 \begin{align*} -\frac{{\left (b x^{4} + a\right )}^{\frac{3}{4}}}{3 \, a x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.47844, size = 43, normalized size = 2.05 \begin{align*} -\frac{{\left (b x^{4} + a\right )}^{\frac{3}{4}}}{3 \, a x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.970609, size = 31, normalized size = 1.48 \begin{align*} \frac{b^{\frac{3}{4}} \left (\frac{a}{b x^{4}} + 1\right )^{\frac{3}{4}} \Gamma \left (- \frac{3}{4}\right )}{4 a \Gamma \left (\frac{1}{4}\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{{\left (b x^{4} + a\right )}^{\frac{1}{4}} x^{4}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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