Optimal. Leaf size=16 \[ \frac{x \log (x)}{b^2 \sqrt{b x^2}} \]
[Out]
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Rubi [A] time = 0.00763255, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{x \log (x)}{b^2 \sqrt{b x^2}} \]
Antiderivative was successfully verified.
[In] Int[x^4/(b*x^2)^(5/2),x]
[Out]
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Rubi in Sympy [A] time = 2.35479, size = 15, normalized size = 0.94 \[ \frac{\sqrt{b x^{2}} \log{\left (x \right )}}{b^{3} x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**4/(b*x**2)**(5/2),x)
[Out]
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Mathematica [A] time = 0.00234548, size = 15, normalized size = 0.94 \[ \frac{x^5 \log (x)}{\left (b x^2\right )^{5/2}} \]
Antiderivative was successfully verified.
[In] Integrate[x^4/(b*x^2)^(5/2),x]
[Out]
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Maple [A] time = 0.006, size = 14, normalized size = 0.9 \[{{x}^{5}\ln \left ( x \right ) \left ( b{x}^{2} \right ) ^{-{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^4/(b*x^2)^(5/2),x)
[Out]
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Maxima [A] time = 1.43954, size = 8, normalized size = 0.5 \[ \frac{\log \left (x\right )}{b^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^4/(b*x^2)^(5/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.242377, size = 22, normalized size = 1.38 \[ \frac{\sqrt{b x^{2}} \log \left (x\right )}{b^{3} x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^4/(b*x^2)^(5/2),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x^{4}}{\left (b x^{2}\right )^{\frac{5}{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**4/(b*x**2)**(5/2),x)
[Out]
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GIAC/XCAS [A] time = 0.234759, size = 28, normalized size = 1.75 \[ -\frac{{\rm ln}\left ({\left | -\sqrt{b} x + \sqrt{b x^{2}} \right |}\right )}{b^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^4/(b*x^2)^(5/2),x, algorithm="giac")
[Out]