Optimal. Leaf size=51 \[ \frac{2}{5} a^3 x^{5/2}+\frac{2}{3} a^2 b x^{9/2}+\frac{6}{13} a b^2 x^{13/2}+\frac{2}{17} b^3 x^{17/2} \]
[Out]
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Rubi [A] time = 0.0431283, antiderivative size = 51, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ \frac{2}{5} a^3 x^{5/2}+\frac{2}{3} a^2 b x^{9/2}+\frac{6}{13} a b^2 x^{13/2}+\frac{2}{17} b^3 x^{17/2} \]
Antiderivative was successfully verified.
[In] Int[x^(3/2)*(a + b*x^2)^3,x]
[Out]
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Rubi in Sympy [A] time = 6.46993, size = 49, normalized size = 0.96 \[ \frac{2 a^{3} x^{\frac{5}{2}}}{5} + \frac{2 a^{2} b x^{\frac{9}{2}}}{3} + \frac{6 a b^{2} x^{\frac{13}{2}}}{13} + \frac{2 b^{3} x^{\frac{17}{2}}}{17} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(3/2)*(b*x**2+a)**3,x)
[Out]
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Mathematica [A] time = 0.0138322, size = 41, normalized size = 0.8 \[ \frac{2 x^{5/2} \left (663 a^3+1105 a^2 b x^2+765 a b^2 x^4+195 b^3 x^6\right )}{3315} \]
Antiderivative was successfully verified.
[In] Integrate[x^(3/2)*(a + b*x^2)^3,x]
[Out]
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Maple [A] time = 0.007, size = 38, normalized size = 0.8 \[{\frac{390\,{b}^{3}{x}^{6}+1530\,a{b}^{2}{x}^{4}+2210\,{a}^{2}b{x}^{2}+1326\,{a}^{3}}{3315}{x}^{{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(3/2)*(b*x^2+a)^3,x)
[Out]
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Maxima [A] time = 1.37484, size = 47, normalized size = 0.92 \[ \frac{2}{17} \, b^{3} x^{\frac{17}{2}} + \frac{6}{13} \, a b^{2} x^{\frac{13}{2}} + \frac{2}{3} \, a^{2} b x^{\frac{9}{2}} + \frac{2}{5} \, a^{3} x^{\frac{5}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^3*x^(3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.210796, size = 54, normalized size = 1.06 \[ \frac{2}{3315} \,{\left (195 \, b^{3} x^{8} + 765 \, a b^{2} x^{6} + 1105 \, a^{2} b x^{4} + 663 \, a^{3} x^{2}\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^3*x^(3/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 20.2958, size = 49, normalized size = 0.96 \[ \frac{2 a^{3} x^{\frac{5}{2}}}{5} + \frac{2 a^{2} b x^{\frac{9}{2}}}{3} + \frac{6 a b^{2} x^{\frac{13}{2}}}{13} + \frac{2 b^{3} x^{\frac{17}{2}}}{17} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(3/2)*(b*x**2+a)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.208302, size = 47, normalized size = 0.92 \[ \frac{2}{17} \, b^{3} x^{\frac{17}{2}} + \frac{6}{13} \, a b^{2} x^{\frac{13}{2}} + \frac{2}{3} \, a^{2} b x^{\frac{9}{2}} + \frac{2}{5} \, a^{3} x^{\frac{5}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^3*x^(3/2),x, algorithm="giac")
[Out]