Optimal. Leaf size=19 \[ -\frac {\sqrt [4]{a+b x^4}}{a x} \]
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Rubi [A] time = 0.01, antiderivative size = 19, 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 = {264} \[ -\frac {\sqrt [4]{a+b x^4}}{a x} \]
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin {align*} \int \frac {1}{x^2 \left (a+b x^4\right )^{3/4}} \, dx &=-\frac {\sqrt [4]{a+b x^4}}{a x}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 19, normalized size = 1.00 \[ -\frac {\sqrt [4]{a+b x^4}}{a x} \]
Antiderivative was successfully verified.
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fricas [A] time = 1.09, size = 17, normalized size = 0.89 \[ -\frac {{\left (b x^{4} + a\right )}^{\frac {1}{4}}}{a x} \]
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 \[ \int \frac {1}{{\left (b x^{4} + a\right )}^{\frac {3}{4}} x^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 18, normalized size = 0.95 \[ -\frac {\left (b \,x^{4}+a \right )^{\frac {1}{4}}}{a x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.33, size = 17, normalized size = 0.89 \[ -\frac {{\left (b x^{4} + a\right )}^{\frac {1}{4}}}{a x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.10, size = 17, normalized size = 0.89 \[ -\frac {{\left (b\,x^4+a\right )}^{1/4}}{a\,x} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 1.21, size = 31, normalized size = 1.63 \[ \frac {\sqrt [4]{b} \sqrt [4]{\frac {a}{b x^{4}} + 1} \Gamma \left (- \frac {1}{4}\right )}{4 a \Gamma \left (\frac {3}{4}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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