Optimal. Leaf size=59 \[ -\frac{2 a^2}{3 b^3 \sqrt{a+b x^3}}-\frac{4 a \sqrt{a+b x^3}}{3 b^3}+\frac{2 \left (a+b x^3\right )^{3/2}}{9 b^3} \]
[Out]
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Rubi [A] time = 0.0886321, antiderivative size = 59, 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 \[ -\frac{2 a^2}{3 b^3 \sqrt{a+b x^3}}-\frac{4 a \sqrt{a+b x^3}}{3 b^3}+\frac{2 \left (a+b x^3\right )^{3/2}}{9 b^3} \]
Antiderivative was successfully verified.
[In] Int[x^8/(a + b*x^3)^(3/2),x]
[Out]
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Rubi in Sympy [A] time = 10.8284, size = 54, normalized size = 0.92 \[ - \frac{2 a^{2}}{3 b^{3} \sqrt{a + b x^{3}}} - \frac{4 a \sqrt{a + b x^{3}}}{3 b^{3}} + \frac{2 \left (a + b x^{3}\right )^{\frac{3}{2}}}{9 b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**8/(b*x**3+a)**(3/2),x)
[Out]
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Mathematica [A] time = 0.0301514, size = 38, normalized size = 0.64 \[ \frac{2 \left (-8 a^2-4 a b x^3+b^2 x^6\right )}{9 b^3 \sqrt{a+b x^3}} \]
Antiderivative was successfully verified.
[In] Integrate[x^8/(a + b*x^3)^(3/2),x]
[Out]
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Maple [A] time = 0.007, size = 36, normalized size = 0.6 \[ -{\frac{-2\,{b}^{2}{x}^{6}+8\,ab{x}^{3}+16\,{a}^{2}}{9\,{b}^{3}}{\frac{1}{\sqrt{b{x}^{3}+a}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^8/(b*x^3+a)^(3/2),x)
[Out]
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Maxima [A] time = 1.43941, size = 63, normalized size = 1.07 \[ \frac{2 \,{\left (b x^{3} + a\right )}^{\frac{3}{2}}}{9 \, b^{3}} - \frac{4 \, \sqrt{b x^{3} + a} a}{3 \, b^{3}} - \frac{2 \, a^{2}}{3 \, \sqrt{b x^{3} + a} b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^8/(b*x^3 + a)^(3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.227429, size = 46, normalized size = 0.78 \[ \frac{2 \,{\left (b^{2} x^{6} - 4 \, a b x^{3} - 8 \, a^{2}\right )}}{9 \, \sqrt{b x^{3} + a} b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^8/(b*x^3 + a)^(3/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 5.48458, size = 70, normalized size = 1.19 \[ \begin{cases} - \frac{16 a^{2}}{9 b^{3} \sqrt{a + b x^{3}}} - \frac{8 a x^{3}}{9 b^{2} \sqrt{a + b x^{3}}} + \frac{2 x^{6}}{9 b \sqrt{a + b x^{3}}} & \text{for}\: b \neq 0 \\\frac{x^{9}}{9 a^{\frac{3}{2}}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**8/(b*x**3+a)**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.235441, size = 55, normalized size = 0.93 \[ \frac{2 \,{\left ({\left (b x^{3} + a\right )}^{\frac{3}{2}} - 6 \, \sqrt{b x^{3} + a} a - \frac{3 \, a^{2}}{\sqrt{b x^{3} + a}}\right )}}{9 \, b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^8/(b*x^3 + a)^(3/2),x, algorithm="giac")
[Out]