Optimal. Leaf size=38 \[ \frac{2 a}{3 b^2 \sqrt{a+b x^3}}+\frac{2 \sqrt{a+b x^3}}{3 b^2} \]
[Out]
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Rubi [A] time = 0.0608243, antiderivative size = 38, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ \frac{2 a}{3 b^2 \sqrt{a+b x^3}}+\frac{2 \sqrt{a+b x^3}}{3 b^2} \]
Antiderivative was successfully verified.
[In] Int[x^5/(a + b*x^3)^(3/2),x]
[Out]
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Rubi in Sympy [A] time = 7.3163, size = 34, normalized size = 0.89 \[ \frac{2 a}{3 b^{2} \sqrt{a + b x^{3}}} + \frac{2 \sqrt{a + b x^{3}}}{3 b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**5/(b*x**3+a)**(3/2),x)
[Out]
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Mathematica [A] time = 0.0213304, size = 27, normalized size = 0.71 \[ \frac{2 \left (2 a+b x^3\right )}{3 b^2 \sqrt{a+b x^3}} \]
Antiderivative was successfully verified.
[In] Integrate[x^5/(a + b*x^3)^(3/2),x]
[Out]
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Maple [A] time = 0.008, size = 24, normalized size = 0.6 \[{\frac{2\,b{x}^{3}+4\,a}{3\,{b}^{2}}{\frac{1}{\sqrt{b{x}^{3}+a}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^5/(b*x^3+a)^(3/2),x)
[Out]
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Maxima [A] time = 1.42177, size = 41, normalized size = 1.08 \[ \frac{2 \, \sqrt{b x^{3} + a}}{3 \, b^{2}} + \frac{2 \, a}{3 \, \sqrt{b x^{3} + a} b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^5/(b*x^3 + a)^(3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.228181, size = 31, normalized size = 0.82 \[ \frac{2 \,{\left (b x^{3} + 2 \, a\right )}}{3 \, \sqrt{b x^{3} + a} b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^5/(b*x^3 + a)^(3/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.00017, size = 46, normalized size = 1.21 \[ \begin{cases} \frac{4 a}{3 b^{2} \sqrt{a + b x^{3}}} + \frac{2 x^{3}}{3 b \sqrt{a + b x^{3}}} & \text{for}\: b \neq 0 \\\frac{x^{6}}{6 a^{\frac{3}{2}}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**5/(b*x**3+a)**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.245199, size = 35, normalized size = 0.92 \[ \frac{2 \,{\left (\sqrt{b x^{3} + a} + \frac{a}{\sqrt{b x^{3} + a}}\right )}}{3 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^5/(b*x^3 + a)^(3/2),x, algorithm="giac")
[Out]