Optimal. Leaf size=101 \[ -\frac{2 a^3 A}{7 x^{7/2}}-\frac{2 a^3 B}{5 x^{5/2}}-\frac{2 a^2 A c}{x^{3/2}}-\frac{6 a^2 B c}{\sqrt{x}}+6 a A c^2 \sqrt{x}+2 a B c^2 x^{3/2}+\frac{2}{5} A c^3 x^{5/2}+\frac{2}{7} B c^3 x^{7/2} \]
[Out]
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Rubi [A] time = 0.0984962, antiderivative size = 101, 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 \[ -\frac{2 a^3 A}{7 x^{7/2}}-\frac{2 a^3 B}{5 x^{5/2}}-\frac{2 a^2 A c}{x^{3/2}}-\frac{6 a^2 B c}{\sqrt{x}}+6 a A c^2 \sqrt{x}+2 a B c^2 x^{3/2}+\frac{2}{5} A c^3 x^{5/2}+\frac{2}{7} B c^3 x^{7/2} \]
Antiderivative was successfully verified.
[In] Int[((A + B*x)*(a + c*x^2)^3)/x^(9/2),x]
[Out]
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Rubi in Sympy [A] time = 11.5136, size = 107, normalized size = 1.06 \[ - \frac{2 A a^{3}}{7 x^{\frac{7}{2}}} - \frac{2 A a^{2} c}{x^{\frac{3}{2}}} + 6 A a c^{2} \sqrt{x} + \frac{2 A c^{3} x^{\frac{5}{2}}}{5} - \frac{2 B a^{3}}{5 x^{\frac{5}{2}}} - \frac{6 B a^{2} c}{\sqrt{x}} + 2 B a c^{2} x^{\frac{3}{2}} + \frac{2 B c^{3} x^{\frac{7}{2}}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((B*x+A)*(c*x**2+a)**3/x**(9/2),x)
[Out]
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Mathematica [A] time = 0.041209, size = 70, normalized size = 0.69 \[ \frac{-2 a^3 (5 A+7 B x)-70 a^2 c x^2 (A+3 B x)+70 a c^2 x^4 (3 A+B x)+2 c^3 x^6 (7 A+5 B x)}{35 x^{7/2}} \]
Antiderivative was successfully verified.
[In] Integrate[((A + B*x)*(a + c*x^2)^3)/x^(9/2),x]
[Out]
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Maple [A] time = 0.008, size = 78, normalized size = 0.8 \[ -{\frac{-10\,B{c}^{3}{x}^{7}-14\,A{c}^{3}{x}^{6}-70\,aB{c}^{2}{x}^{5}-210\,aA{c}^{2}{x}^{4}+210\,{a}^{2}Bc{x}^{3}+70\,{a}^{2}Ac{x}^{2}+14\,{a}^{3}Bx+10\,A{a}^{3}}{35}{x}^{-{\frac{7}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((B*x+A)*(c*x^2+a)^3/x^(9/2),x)
[Out]
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Maxima [A] time = 0.689619, size = 105, normalized size = 1.04 \[ \frac{2}{7} \, B c^{3} x^{\frac{7}{2}} + \frac{2}{5} \, A c^{3} x^{\frac{5}{2}} + 2 \, B a c^{2} x^{\frac{3}{2}} + 6 \, A a c^{2} \sqrt{x} - \frac{2 \,{\left (105 \, B a^{2} c x^{3} + 35 \, A a^{2} c x^{2} + 7 \, B a^{3} x + 5 \, A a^{3}\right )}}{35 \, x^{\frac{7}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + a)^3*(B*x + A)/x^(9/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.268571, size = 104, normalized size = 1.03 \[ \frac{2 \,{\left (5 \, B c^{3} x^{7} + 7 \, A c^{3} x^{6} + 35 \, B a c^{2} x^{5} + 105 \, A a c^{2} x^{4} - 105 \, B a^{2} c x^{3} - 35 \, A a^{2} c x^{2} - 7 \, B a^{3} x - 5 \, A a^{3}\right )}}{35 \, x^{\frac{7}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + a)^3*(B*x + A)/x^(9/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 21.5597, size = 107, normalized size = 1.06 \[ - \frac{2 A a^{3}}{7 x^{\frac{7}{2}}} - \frac{2 A a^{2} c}{x^{\frac{3}{2}}} + 6 A a c^{2} \sqrt{x} + \frac{2 A c^{3} x^{\frac{5}{2}}}{5} - \frac{2 B a^{3}}{5 x^{\frac{5}{2}}} - \frac{6 B a^{2} c}{\sqrt{x}} + 2 B a c^{2} x^{\frac{3}{2}} + \frac{2 B c^{3} x^{\frac{7}{2}}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x+A)*(c*x**2+a)**3/x**(9/2),x)
[Out]
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GIAC/XCAS [A] time = 0.272813, size = 105, normalized size = 1.04 \[ \frac{2}{7} \, B c^{3} x^{\frac{7}{2}} + \frac{2}{5} \, A c^{3} x^{\frac{5}{2}} + 2 \, B a c^{2} x^{\frac{3}{2}} + 6 \, A a c^{2} \sqrt{x} - \frac{2 \,{\left (105 \, B a^{2} c x^{3} + 35 \, A a^{2} c x^{2} + 7 \, B a^{3} x + 5 \, A a^{3}\right )}}{35 \, x^{\frac{7}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + a)^3*(B*x + A)/x^(9/2),x, algorithm="giac")
[Out]