Optimal. Leaf size=23 \[ -\frac {2 \sqrt {a+b x^5}}{5 a x^{5/2}} \]
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Rubi [A] time = 0.00, antiderivative size = 23, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.01, size = 23, normalized size = 1.00 \[ -\frac {2 \sqrt {a+b x^5}}{5 a x^{5/2}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.87, size = 17, normalized size = 0.74 \[ -\frac {2 \, \sqrt {b x^{5} + a}}{5 \, a x^{\frac {5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 23, normalized size = 1.00 \[ -\frac {2 \, \sqrt {b + \frac {a}{x^{5}}}}{5 \, a} + \frac {2 \, \sqrt {b}}{5 \, a} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 18, normalized size = 0.78 \[ -\frac {2 \sqrt {b \,x^{5}+a}}{5 a \,x^{\frac {5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.01, size = 17, normalized size = 0.74 \[ -\frac {2 \, \sqrt {b x^{5} + a}}{5 \, a x^{\frac {5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {1}{x^{7/2}\,\sqrt {b\,x^5+a}} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 7.21, size = 22, normalized size = 0.96 \[ - \frac {2 \sqrt {b} \sqrt {\frac {a}{b x^{5}} + 1}}{5 a} \]
Verification of antiderivative is not currently implemented for this CAS.
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