Optimal. Leaf size=22 \[ -\frac {\left (a-b x^4\right )^{3/4}}{3 a x^3} \]
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Rubi [A] time = 0.00, antiderivative size = 22, 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 = {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*}
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Mathematica [A] time = 0.00, size = 22, normalized size = 1.00 \[ -\frac {\left (a-b x^4\right )^{3/4}}{3 a x^3} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.52, size = 18, normalized size = 0.82 \[ -\frac {{\left (-b x^{4} + a\right )}^{\frac {3}{4}}}{3 \, a x^{3}} \]
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 \[ \int \frac {1}{{\left (-b x^{4} + a\right )}^{\frac {1}{4}} x^{4}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 19, normalized size = 0.86 \[ -\frac {\left (-b \,x^{4}+a \right )^{\frac {3}{4}}}{3 a \,x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.99, size = 18, normalized size = 0.82 \[ -\frac {{\left (-b x^{4} + a\right )}^{\frac {3}{4}}}{3 \, a x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.09, size = 18, normalized size = 0.82 \[ -\frac {{\left (a-b\,x^4\right )}^{3/4}}{3\,a\,x^3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.55, size = 78, normalized size = 3.55 \[ \begin {cases} \frac {b^{\frac {3}{4}} \left (\frac {a}{b x^{4}} - 1\right )^{\frac {3}{4}} \Gamma \left (- \frac {3}{4}\right )}{4 a \Gamma \left (\frac {1}{4}\right )} & \text {for}\: \left |{\frac {a}{b x^{4}}}\right | > 1 \\- \frac {b^{\frac {3}{4}} \left (- \frac {a}{b x^{4}} + 1\right )^{\frac {3}{4}} e^{- \frac {i \pi }{4}} \Gamma \left (- \frac {3}{4}\right )}{4 a \Gamma \left (\frac {1}{4}\right )} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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