Optimal. Leaf size=57 \[ \frac{x^{5/2} \sqrt{a+b x^5}}{5 b}-\frac{a \tanh ^{-1}\left (\frac{\sqrt{b} x^{5/2}}{\sqrt{a+b x^5}}\right )}{5 b^{3/2}} \]
[Out]
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Rubi [A] time = 0.0885204, antiderivative size = 57, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 5, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.294 \[ \frac{x^{5/2} \sqrt{a+b x^5}}{5 b}-\frac{a \tanh ^{-1}\left (\frac{\sqrt{b} x^{5/2}}{\sqrt{a+b x^5}}\right )}{5 b^{3/2}} \]
Antiderivative was successfully verified.
[In] Int[x^(13/2)/Sqrt[a + b*x^5],x]
[Out]
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Rubi in Sympy [A] time = 8.75827, size = 48, normalized size = 0.84 \[ - \frac{a \operatorname{atanh}{\left (\frac{\sqrt{b} x^{\frac{5}{2}}}{\sqrt{a + b x^{5}}} \right )}}{5 b^{\frac{3}{2}}} + \frac{x^{\frac{5}{2}} \sqrt{a + b x^{5}}}{5 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(13/2)/(b*x**5+a)**(1/2),x)
[Out]
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Mathematica [A] time = 0.10126, size = 57, normalized size = 1. \[ \frac{x^{5/2} \sqrt{a+b x^5}}{5 b}-\frac{a \tanh ^{-1}\left (\frac{\sqrt{b} x^{5/2}}{\sqrt{a+b x^5}}\right )}{5 b^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[x^(13/2)/Sqrt[a + b*x^5],x]
[Out]
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Maple [F] time = 0.053, size = 0, normalized size = 0. \[ \int{1{x}^{{\frac{13}{2}}}{\frac{1}{\sqrt{b{x}^{5}+a}}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(13/2)/(b*x^5+a)^(1/2),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^(13/2)/sqrt(b*x^5 + a),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.720871, size = 1, normalized size = 0.02 \[ \left [\frac{4 \, \sqrt{b x^{5} + a} \sqrt{b} x^{\frac{5}{2}} + a \log \left (4 \,{\left (2 \, b^{2} x^{7} + a b x^{2}\right )} \sqrt{b x^{5} + a} \sqrt{x} -{\left (8 \, b^{2} x^{10} + 8 \, a b x^{5} + a^{2}\right )} \sqrt{b}\right )}{20 \, b^{\frac{3}{2}}}, \frac{2 \, \sqrt{b x^{5} + a} \sqrt{-b} x^{\frac{5}{2}} - a \arctan \left (\frac{2 \, \sqrt{b x^{5} + a} \sqrt{-b} x^{\frac{5}{2}}}{2 \, b x^{5} + a}\right )}{10 \, \sqrt{-b} b}\right ] \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^(13/2)/sqrt(b*x^5 + a),x, algorithm="fricas")
[Out]
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(13/2)/(b*x**5+a)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.250401, size = 59, normalized size = 1.04 \[ \frac{\sqrt{b x^{5} + a} x^{\frac{5}{2}}}{5 \, b} + \frac{a{\rm ln}\left ({\left | -\sqrt{b} x^{\frac{5}{2}} + \sqrt{b x^{5} + a} \right |}\right )}{5 \, b^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^(13/2)/sqrt(b*x^5 + a),x, algorithm="giac")
[Out]