Optimal. Leaf size=77 \[ \frac{2}{9} a^2 A x^{9/2}+\frac{2}{11} a^2 B x^{11/2}+\frac{4}{13} a A c x^{13/2}+\frac{4}{15} a B c x^{15/2}+\frac{2}{17} A c^2 x^{17/2}+\frac{2}{19} B c^2 x^{19/2} \]
[Out]
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Rubi [A] time = 0.0730284, antiderivative size = 77, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ \frac{2}{9} a^2 A x^{9/2}+\frac{2}{11} a^2 B x^{11/2}+\frac{4}{13} a A c x^{13/2}+\frac{4}{15} a B c x^{15/2}+\frac{2}{17} A c^2 x^{17/2}+\frac{2}{19} B c^2 x^{19/2} \]
Antiderivative was successfully verified.
[In] Int[x^(7/2)*(A + B*x)*(a + c*x^2)^2,x]
[Out]
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Rubi in Sympy [A] time = 8.77924, size = 80, normalized size = 1.04 \[ \frac{2 A a^{2} x^{\frac{9}{2}}}{9} + \frac{4 A a c x^{\frac{13}{2}}}{13} + \frac{2 A c^{2} x^{\frac{17}{2}}}{17} + \frac{2 B a^{2} x^{\frac{11}{2}}}{11} + \frac{4 B a c x^{\frac{15}{2}}}{15} + \frac{2 B c^{2} x^{\frac{19}{2}}}{19} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(7/2)*(B*x+A)*(c*x**2+a)**2,x)
[Out]
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Mathematica [A] time = 0.0411556, size = 60, normalized size = 0.78 \[ \frac{2}{99} a^2 x^{9/2} (11 A+9 B x)+\frac{4}{195} a c x^{13/2} (15 A+13 B x)+\frac{2}{323} c^2 x^{17/2} (19 A+17 B x) \]
Antiderivative was successfully verified.
[In] Integrate[x^(7/2)*(A + B*x)*(a + c*x^2)^2,x]
[Out]
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Maple [A] time = 0.009, size = 54, normalized size = 0.7 \[{\frac{218790\,B{c}^{2}{x}^{5}+244530\,A{c}^{2}{x}^{4}+554268\,aBc{x}^{3}+639540\,aAc{x}^{2}+377910\,{a}^{2}Bx+461890\,A{a}^{2}}{2078505}{x}^{{\frac{9}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(7/2)*(B*x+A)*(c*x^2+a)^2,x)
[Out]
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Maxima [A] time = 0.684646, size = 72, normalized size = 0.94 \[ \frac{2}{19} \, B c^{2} x^{\frac{19}{2}} + \frac{2}{17} \, A c^{2} x^{\frac{17}{2}} + \frac{4}{15} \, B a c x^{\frac{15}{2}} + \frac{4}{13} \, A a c x^{\frac{13}{2}} + \frac{2}{11} \, B a^{2} x^{\frac{11}{2}} + \frac{2}{9} \, A a^{2} x^{\frac{9}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + a)^2*(B*x + A)*x^(7/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.273964, size = 78, normalized size = 1.01 \[ \frac{2}{2078505} \,{\left (109395 \, B c^{2} x^{9} + 122265 \, A c^{2} x^{8} + 277134 \, B a c x^{7} + 319770 \, A a c x^{6} + 188955 \, B a^{2} x^{5} + 230945 \, A a^{2} x^{4}\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + a)^2*(B*x + A)*x^(7/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 41.4049, size = 80, normalized size = 1.04 \[ \frac{2 A a^{2} x^{\frac{9}{2}}}{9} + \frac{4 A a c x^{\frac{13}{2}}}{13} + \frac{2 A c^{2} x^{\frac{17}{2}}}{17} + \frac{2 B a^{2} x^{\frac{11}{2}}}{11} + \frac{4 B a c x^{\frac{15}{2}}}{15} + \frac{2 B c^{2} x^{\frac{19}{2}}}{19} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(7/2)*(B*x+A)*(c*x**2+a)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.268402, size = 72, normalized size = 0.94 \[ \frac{2}{19} \, B c^{2} x^{\frac{19}{2}} + \frac{2}{17} \, A c^{2} x^{\frac{17}{2}} + \frac{4}{15} \, B a c x^{\frac{15}{2}} + \frac{4}{13} \, A a c x^{\frac{13}{2}} + \frac{2}{11} \, B a^{2} x^{\frac{11}{2}} + \frac{2}{9} \, A a^{2} x^{\frac{9}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + a)^2*(B*x + A)*x^(7/2),x, algorithm="giac")
[Out]