Optimal. Leaf size=78 \[ \frac{2 a^3}{3 b^4 \sqrt{a+b x^3}}+\frac{2 a^2 \sqrt{a+b x^3}}{b^4}-\frac{2 a \left (a+b x^3\right )^{3/2}}{3 b^4}+\frac{2 \left (a+b x^3\right )^{5/2}}{15 b^4} \]
[Out]
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Rubi [A] time = 0.111452, antiderivative size = 78, 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 \[ \frac{2 a^3}{3 b^4 \sqrt{a+b x^3}}+\frac{2 a^2 \sqrt{a+b x^3}}{b^4}-\frac{2 a \left (a+b x^3\right )^{3/2}}{3 b^4}+\frac{2 \left (a+b x^3\right )^{5/2}}{15 b^4} \]
Antiderivative was successfully verified.
[In] Int[x^11/(a + b*x^3)^(3/2),x]
[Out]
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Rubi in Sympy [A] time = 14.9627, size = 73, normalized size = 0.94 \[ \frac{2 a^{3}}{3 b^{4} \sqrt{a + b x^{3}}} + \frac{2 a^{2} \sqrt{a + b x^{3}}}{b^{4}} - \frac{2 a \left (a + b x^{3}\right )^{\frac{3}{2}}}{3 b^{4}} + \frac{2 \left (a + b x^{3}\right )^{\frac{5}{2}}}{15 b^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**11/(b*x**3+a)**(3/2),x)
[Out]
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Mathematica [A] time = 0.0370566, size = 49, normalized size = 0.63 \[ \frac{2 \left (16 a^3+8 a^2 b x^3-2 a b^2 x^6+b^3 x^9\right )}{15 b^4 \sqrt{a+b x^3}} \]
Antiderivative was successfully verified.
[In] Integrate[x^11/(a + b*x^3)^(3/2),x]
[Out]
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Maple [A] time = 0.01, size = 46, normalized size = 0.6 \[{\frac{2\,{b}^{3}{x}^{9}-4\,a{b}^{2}{x}^{6}+16\,{a}^{2}b{x}^{3}+32\,{a}^{3}}{15\,{b}^{4}}{\frac{1}{\sqrt{b{x}^{3}+a}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^11/(b*x^3+a)^(3/2),x)
[Out]
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Maxima [A] time = 1.41945, size = 86, normalized size = 1.1 \[ \frac{2 \,{\left (b x^{3} + a\right )}^{\frac{5}{2}}}{15 \, b^{4}} - \frac{2 \,{\left (b x^{3} + a\right )}^{\frac{3}{2}} a}{3 \, b^{4}} + \frac{2 \, \sqrt{b x^{3} + a} a^{2}}{b^{4}} + \frac{2 \, a^{3}}{3 \, \sqrt{b x^{3} + a} b^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^11/(b*x^3 + a)^(3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.229177, size = 61, normalized size = 0.78 \[ \frac{2 \,{\left (b^{3} x^{9} - 2 \, a b^{2} x^{6} + 8 \, a^{2} b x^{3} + 16 \, a^{3}\right )}}{15 \, \sqrt{b x^{3} + a} b^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^11/(b*x^3 + a)^(3/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 11.2718, size = 94, normalized size = 1.21 \[ \begin{cases} \frac{32 a^{3}}{15 b^{4} \sqrt{a + b x^{3}}} + \frac{16 a^{2} x^{3}}{15 b^{3} \sqrt{a + b x^{3}}} - \frac{4 a x^{6}}{15 b^{2} \sqrt{a + b x^{3}}} + \frac{2 x^{9}}{15 b \sqrt{a + b x^{3}}} & \text{for}\: b \neq 0 \\\frac{x^{12}}{12 a^{\frac{3}{2}}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**11/(b*x**3+a)**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.214355, size = 74, normalized size = 0.95 \[ \frac{2 \,{\left ({\left (b x^{3} + a\right )}^{\frac{5}{2}} - 5 \,{\left (b x^{3} + a\right )}^{\frac{3}{2}} a + 15 \, \sqrt{b x^{3} + a} a^{2} + \frac{5 \, a^{3}}{\sqrt{b x^{3} + a}}\right )}}{15 \, b^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^11/(b*x^3 + a)^(3/2),x, algorithm="giac")
[Out]