Optimal. Leaf size=23 \[ -\frac{2 \sqrt{a+b x^5}}{5 a x^{5/2}} \]
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Rubi [A] time = 0.0047669, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059, Rules used = {264} \[ -\frac{2 \sqrt{a+b x^5}}{5 a x^{5/2}} \]
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin{align*} \int \frac{1}{x^{7/2} \sqrt{a+b x^5}} \, dx &=-\frac{2 \sqrt{a+b x^5}}{5 a x^{5/2}}\\ \end{align*}
Mathematica [A] time = 0.0048548, size = 23, normalized size = 1. \[ -\frac{2 \sqrt{a+b x^5}}{5 a x^{5/2}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 18, normalized size = 0.8 \begin{align*} -{\frac{2}{5\,a}\sqrt{b{x}^{5}+a}{x}^{-{\frac{5}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.96917, size = 23, normalized size = 1. \begin{align*} -\frac{2 \, \sqrt{b x^{5} + a}}{5 \, a x^{\frac{5}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.66232, size = 46, normalized size = 2. \begin{align*} -\frac{2 \, \sqrt{b x^{5} + a}}{5 \, a x^{\frac{5}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 27.6844, size = 22, normalized size = 0.96 \begin{align*} - \frac{2 \sqrt{b} \sqrt{\frac{a}{b x^{5}} + 1}}{5 a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.16133, size = 31, normalized size = 1.35 \begin{align*} -\frac{2 \, \sqrt{b + \frac{a}{x^{5}}}}{5 \, a} + \frac{2 \, \sqrt{b}}{5 \, a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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