Optimal. Leaf size=23 \[ -\frac {2}{5} x \sqrt {x^5+1} \sqrt {\frac {a}{x^7}} \]
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Rubi [A] time = 0.00, antiderivative size = 23, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.105, Rules used = {15, 264} \[ -\frac {2}{5} x \sqrt {x^5+1} \sqrt {\frac {a}{x^7}} \]
Antiderivative was successfully verified.
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Rule 15
Rule 264
Rubi steps
\begin {align*} \int \frac {\sqrt {\frac {a}{x^7}}}{\sqrt {1+x^5}} \, dx &=\left (\sqrt {\frac {a}{x^7}} x^{7/2}\right ) \int \frac {1}{x^{7/2} \sqrt {1+x^5}} \, dx\\ &=-\frac {2}{5} \sqrt {\frac {a}{x^7}} x \sqrt {1+x^5}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 23, normalized size = 1.00 \[ -\frac {2}{5} x \sqrt {x^5+1} \sqrt {\frac {a}{x^7}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.45, size = 17, normalized size = 0.74 \[ -\frac {2}{5} \, \sqrt {x^{5} + 1} x \sqrt {\frac {a}{x^{7}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.24, size = 28, normalized size = 1.22 \[ -\frac {2 \, a^{4} {\left (\frac {\sqrt {a + \frac {a}{x^{5}}}}{a^{3}} - \frac {1}{a^{\frac {5}{2}}}\right )}}{5 \, {\left | a \right |}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.00, size = 37, normalized size = 1.61 \[ -\frac {2 \left (x +1\right ) \left (x^{4}-x^{3}+x^{2}-x +1\right ) \sqrt {\frac {a}{x^{7}}}\, x}{5 \sqrt {x^{5}+1}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 2.22, size = 41, normalized size = 1.78 \[ -\frac {2 \, {\left (\sqrt {a} x^{6} + \sqrt {a} x\right )}}{5 \, \sqrt {x^{4} - x^{3} + x^{2} - x + 1} \sqrt {x + 1} x^{\frac {7}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.69, size = 17, normalized size = 0.74 \[ -\frac {2\,x\,\sqrt {x^5+1}\,\sqrt {\frac {a}{x^7}}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\sqrt {\frac {a}{x^{7}}}}{\sqrt {\left (x + 1\right ) \left (x^{4} - x^{3} + x^{2} - x + 1\right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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