Optimal. Leaf size=14 \[ \frac {g x}{\sqrt {a+b x^4}} \]
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Rubi [A] time = 0.01, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {383} \[ \frac {g x}{\sqrt {a+b x^4}} \]
Antiderivative was successfully verified.
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Rule 383
Rubi steps
\begin {align*} \int \frac {a g-b g x^4}{\left (a+b x^4\right )^{3/2}} \, dx &=\frac {g x}{\sqrt {a+b x^4}}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 14, normalized size = 1.00 \[ \frac {g x}{\sqrt {a+b x^4}} \]
Antiderivative was successfully verified.
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fricas [A] time = 1.06, size = 12, normalized size = 0.86 \[ \frac {g x}{\sqrt {b x^{4} + a}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.20, size = 12, normalized size = 0.86 \[ \frac {g x}{\sqrt {b x^{4} + a}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 13, normalized size = 0.93 \[ \frac {g x}{\sqrt {b \,x^{4}+a}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.76, size = 12, normalized size = 0.86 \[ \frac {g x}{\sqrt {b x^{4} + a}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.04, size = 12, normalized size = 0.86 \[ \frac {g\,x}{\sqrt {b\,x^4+a}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [C] time = 9.60, size = 80, normalized size = 5.71 \[ \frac {g x \Gamma \left (\frac {1}{4}\right ) {{}_{2}F_{1}\left (\begin {matrix} \frac {1}{4}, \frac {3}{2} \\ \frac {5}{4} \end {matrix}\middle | {\frac {b x^{4} e^{i \pi }}{a}} \right )}}{4 \sqrt {a} \Gamma \left (\frac {5}{4}\right )} - \frac {b g x^{5} \Gamma \left (\frac {5}{4}\right ) {{}_{2}F_{1}\left (\begin {matrix} \frac {5}{4}, \frac {3}{2} \\ \frac {9}{4} \end {matrix}\middle | {\frac {b x^{4} e^{i \pi }}{a}} \right )}}{4 a^{\frac {3}{2}} \Gamma \left (\frac {9}{4}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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