Optimal. Leaf size=55 \[ \frac{2}{11} x^{11/2} (a B+A b)+\frac{2}{9} a A x^{9/2}+\frac{2}{13} x^{13/2} (A c+b B)+\frac{2}{15} B c x^{15/2} \]
[Out]
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Rubi [A] time = 0.0683762, antiderivative size = 55, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.048 \[ \frac{2}{11} x^{11/2} (a B+A b)+\frac{2}{9} a A x^{9/2}+\frac{2}{13} x^{13/2} (A c+b B)+\frac{2}{15} B c x^{15/2} \]
Antiderivative was successfully verified.
[In] Int[x^(7/2)*(A + B*x)*(a + b*x + c*x^2),x]
[Out]
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Rubi in Sympy [A] time = 8.36332, size = 60, normalized size = 1.09 \[ \frac{2 A a x^{\frac{9}{2}}}{9} + \frac{2 B c x^{\frac{15}{2}}}{15} + x^{\frac{13}{2}} \left (\frac{2 A c}{13} + \frac{2 B b}{13}\right ) + x^{\frac{11}{2}} \left (\frac{2 A b}{11} + \frac{2 B a}{11}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(7/2)*(B*x+A)*(c*x**2+b*x+a),x)
[Out]
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Mathematica [A] time = 0.0324018, size = 43, normalized size = 0.78 \[ \frac{2 x^{9/2} \left (585 x (a B+A b)+715 a A+495 x^2 (A c+b B)+429 B c x^3\right )}{6435} \]
Antiderivative was successfully verified.
[In] Integrate[x^(7/2)*(A + B*x)*(a + b*x + c*x^2),x]
[Out]
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Maple [A] time = 0.004, size = 42, normalized size = 0.8 \[{\frac{858\,Bc{x}^{3}+990\,Ac{x}^{2}+990\,Bb{x}^{2}+1170\,Abx+1170\,aBx+1430\,aA}{6435}{x}^{{\frac{9}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(7/2)*(B*x+A)*(c*x^2+b*x+a),x)
[Out]
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Maxima [A] time = 0.722887, size = 53, normalized size = 0.96 \[ \frac{2}{15} \, B c x^{\frac{15}{2}} + \frac{2}{13} \,{\left (B b + A c\right )} x^{\frac{13}{2}} + \frac{2}{9} \, A a x^{\frac{9}{2}} + \frac{2}{11} \,{\left (B a + A b\right )} x^{\frac{11}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)*(B*x + A)*x^(7/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.271709, size = 59, normalized size = 1.07 \[ \frac{2}{6435} \,{\left (429 \, B c x^{7} + 495 \,{\left (B b + A c\right )} x^{6} + 715 \, A a x^{4} + 585 \,{\left (B a + A b\right )} x^{5}\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)*(B*x + A)*x^(7/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 20.4043, size = 70, normalized size = 1.27 \[ \frac{2 A a x^{\frac{9}{2}}}{9} + \frac{2 A b x^{\frac{11}{2}}}{11} + \frac{2 A c x^{\frac{13}{2}}}{13} + \frac{2 B a x^{\frac{11}{2}}}{11} + \frac{2 B b x^{\frac{13}{2}}}{13} + \frac{2 B c x^{\frac{15}{2}}}{15} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(7/2)*(B*x+A)*(c*x**2+b*x+a),x)
[Out]
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GIAC/XCAS [A] time = 0.268345, size = 58, normalized size = 1.05 \[ \frac{2}{15} \, B c x^{\frac{15}{2}} + \frac{2}{13} \, B b x^{\frac{13}{2}} + \frac{2}{13} \, A c x^{\frac{13}{2}} + \frac{2}{11} \, B a x^{\frac{11}{2}} + \frac{2}{11} \, A b x^{\frac{11}{2}} + \frac{2}{9} \, A a x^{\frac{9}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)*(B*x + A)*x^(7/2),x, algorithm="giac")
[Out]