Optimal. Leaf size=51 \[ \frac{2}{9} a^3 x^{9/2}+\frac{6}{13} a^2 b x^{13/2}+\frac{6}{17} a b^2 x^{17/2}+\frac{2}{21} b^3 x^{21/2} \]
[Out]
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Rubi [A] time = 0.0425014, 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 \[ \frac{2}{9} a^3 x^{9/2}+\frac{6}{13} a^2 b x^{13/2}+\frac{6}{17} a b^2 x^{17/2}+\frac{2}{21} b^3 x^{21/2} \]
Antiderivative was successfully verified.
[In] Int[x^(7/2)*(a + b*x^2)^3,x]
[Out]
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Rubi in Sympy [A] time = 6.35518, size = 49, normalized size = 0.96 \[ \frac{2 a^{3} x^{\frac{9}{2}}}{9} + \frac{6 a^{2} b x^{\frac{13}{2}}}{13} + \frac{6 a b^{2} x^{\frac{17}{2}}}{17} + \frac{2 b^{3} x^{\frac{21}{2}}}{21} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(7/2)*(b*x**2+a)**3,x)
[Out]
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Mathematica [A] time = 0.0143093, size = 41, normalized size = 0.8 \[ \frac{2 x^{9/2} \left (1547 a^3+3213 a^2 b x^2+2457 a b^2 x^4+663 b^3 x^6\right )}{13923} \]
Antiderivative was successfully verified.
[In] Integrate[x^(7/2)*(a + b*x^2)^3,x]
[Out]
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Maple [A] time = 0.008, size = 38, normalized size = 0.8 \[{\frac{1326\,{b}^{3}{x}^{6}+4914\,a{b}^{2}{x}^{4}+6426\,{a}^{2}b{x}^{2}+3094\,{a}^{3}}{13923}{x}^{{\frac{9}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(7/2)*(b*x^2+a)^3,x)
[Out]
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Maxima [A] time = 1.34791, size = 47, normalized size = 0.92 \[ \frac{2}{21} \, b^{3} x^{\frac{21}{2}} + \frac{6}{17} \, a b^{2} x^{\frac{17}{2}} + \frac{6}{13} \, a^{2} b x^{\frac{13}{2}} + \frac{2}{9} \, a^{3} x^{\frac{9}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^3*x^(7/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.211878, size = 54, normalized size = 1.06 \[ \frac{2}{13923} \,{\left (663 \, b^{3} x^{10} + 2457 \, a b^{2} x^{8} + 3213 \, a^{2} b x^{6} + 1547 \, a^{3} x^{4}\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^3*x^(7/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 70.7934, size = 49, normalized size = 0.96 \[ \frac{2 a^{3} x^{\frac{9}{2}}}{9} + \frac{6 a^{2} b x^{\frac{13}{2}}}{13} + \frac{6 a b^{2} x^{\frac{17}{2}}}{17} + \frac{2 b^{3} x^{\frac{21}{2}}}{21} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(7/2)*(b*x**2+a)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.206874, size = 47, normalized size = 0.92 \[ \frac{2}{21} \, b^{3} x^{\frac{21}{2}} + \frac{6}{17} \, a b^{2} x^{\frac{17}{2}} + \frac{6}{13} \, a^{2} b x^{\frac{13}{2}} + \frac{2}{9} \, a^{3} x^{\frac{9}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^3*x^(7/2),x, algorithm="giac")
[Out]