Optimal. Leaf size=18 \[ -\frac{2}{3} \left (\frac{1}{x^5}+\frac{1}{x^4}\right )^{3/2} x^6 \]
[Out]
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Rubi [A] time = 0.0155205, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182 \[ -\frac{2}{3} \left (\frac{1}{x^5}+\frac{1}{x^4}\right )^{3/2} x^6 \]
Antiderivative was successfully verified.
[In] Int[Sqrt[(1 + x)/x^5],x]
[Out]
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Rubi in Sympy [A] time = 1.18497, size = 20, normalized size = 1.11 \[ - \frac{2 x^{6} \left (\frac{1}{x^{4}} + \frac{1}{x^{5}}\right )^{\frac{3}{2}}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(((1+x)/x**5)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0119901, size = 18, normalized size = 1. \[ -\frac{2}{3} x^6 \left (\frac{x+1}{x^5}\right )^{3/2} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[(1 + x)/x^5],x]
[Out]
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Maple [A] time = 0.006, size = 16, normalized size = 0.9 \[ -{\frac{2\,x \left ( 1+x \right ) }{3}\sqrt{{\frac{1+x}{{x}^{5}}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(((1+x)/x^5)^(1/2),x)
[Out]
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Maxima [A] time = 1.41484, size = 14, normalized size = 0.78 \[ -\frac{2 \,{\left (x + 1\right )}^{\frac{3}{2}}}{3 \, x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt((x + 1)/x^5),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.227398, size = 22, normalized size = 1.22 \[ -\frac{2}{3} \,{\left (x^{2} + x\right )} \sqrt{\frac{x + 1}{x^{5}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt((x + 1)/x^5),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \sqrt{\frac{x + 1}{x^{5}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(((1+x)/x**5)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.229375, size = 68, normalized size = 3.78 \[ \frac{2 \,{\left (3 \,{\left (x - \sqrt{x^{2} + x}\right )}^{2}{\rm sign}\left (x\right ) + 3 \,{\left (x - \sqrt{x^{2} + x}\right )}{\rm sign}\left (x\right ) +{\rm sign}\left (x\right )\right )}}{3 \,{\left (x - \sqrt{x^{2} + x}\right )}^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt((x + 1)/x^5),x, algorithm="giac")
[Out]