Optimal. Leaf size=49 \[ \frac{4}{15} x^6 \sqrt{x^5+1} \sqrt{\frac{a}{x^{17}}}-\frac{2}{15} x \sqrt{x^5+1} \sqrt{\frac{a}{x^{17}}} \]
[Out]
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Rubi [A] time = 0.0302922, antiderivative size = 49, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.158 \[ \frac{4}{15} x^6 \sqrt{x^5+1} \sqrt{\frac{a}{x^{17}}}-\frac{2}{15} x \sqrt{x^5+1} \sqrt{\frac{a}{x^{17}}} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[a/x^17]/Sqrt[1 + x^5],x]
[Out]
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Rubi in Sympy [A] time = 8.22471, size = 44, normalized size = 0.9 \[ \frac{4 x^{6} \sqrt{\frac{a}{x^{17}}} \sqrt{x^{5} + 1}}{15} - \frac{2 x \sqrt{\frac{a}{x^{17}}} \sqrt{x^{5} + 1}}{15} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a/x**17)**(1/2)/(x**5+1)**(1/2),x)
[Out]
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Mathematica [A] time = 0.014932, size = 30, normalized size = 0.61 \[ \frac{2}{15} x \sqrt{x^5+1} \left (2 x^5-1\right ) \sqrt{\frac{a}{x^{17}}} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[a/x^17]/Sqrt[1 + x^5],x]
[Out]
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Maple [A] time = 0.008, size = 44, normalized size = 0.9 \[{\frac{2\,x \left ( 1+x \right ) \left ({x}^{4}-{x}^{3}+{x}^{2}-x+1 \right ) \left ( 2\,{x}^{5}-1 \right ) }{15}\sqrt{{\frac{a}{{x}^{17}}}}{\frac{1}{\sqrt{{x}^{5}+1}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a/x^17)^(1/2)/(x^5+1)^(1/2),x)
[Out]
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Maxima [A] time = 0.782597, size = 68, normalized size = 1.39 \[ \frac{2 \,{\left (2 \, \sqrt{a} x^{11} + \sqrt{a} x^{6} - \sqrt{a} x\right )}}{15 \, \sqrt{x^{4} - x^{3} + x^{2} - x + 1} \sqrt{x + 1} x^{\frac{17}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(a/x^17)/sqrt(x^5 + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.276903, size = 34, normalized size = 0.69 \[ \frac{2}{15} \,{\left (2 \, x^{6} - x\right )} \sqrt{x^{5} + 1} \sqrt{\frac{a}{x^{17}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(a/x^17)/sqrt(x^5 + 1),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{\frac{a}{x^{17}}}}{\sqrt{\left (x + 1\right ) \left (x^{4} - x^{3} + x^{2} - x + 1\right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a/x**17)**(1/2)/(x**5+1)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.279049, size = 58, normalized size = 1.18 \[ -\frac{2 \, a^{3}{\left (\frac{2}{a^{\frac{3}{2}}} + \frac{{\left (a + \frac{a}{x^{5}}\right )}^{\frac{3}{2}} - 3 \, \sqrt{a + \frac{a}{x^{5}}} a}{a^{3}}\right )}{\rm sign}\left (x\right )}{15 \,{\left | a \right |}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(a/x^17)/sqrt(x^5 + 1),x, algorithm="giac")
[Out]