Optimal. Leaf size=55 \[ -\frac{a^4 c^3}{7 x^7}+\frac{a^3 b c^3}{3 x^6}-\frac{a b^3 c^3}{2 x^4}+\frac{b^4 c^3}{3 x^3} \]
[Out]
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Rubi [A] time = 0.0664601, antiderivative size = 55, 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 \[ -\frac{a^4 c^3}{7 x^7}+\frac{a^3 b c^3}{3 x^6}-\frac{a b^3 c^3}{2 x^4}+\frac{b^4 c^3}{3 x^3} \]
Antiderivative was successfully verified.
[In] Int[((a + b*x)*(a*c - b*c*x)^3)/x^8,x]
[Out]
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Rubi in Sympy [A] time = 19.5576, size = 49, normalized size = 0.89 \[ - \frac{a^{4} c^{3}}{7 x^{7}} + \frac{a^{3} b c^{3}}{3 x^{6}} - \frac{a b^{3} c^{3}}{2 x^{4}} + \frac{b^{4} c^{3}}{3 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)*(-b*c*x+a*c)**3/x**8,x)
[Out]
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Mathematica [A] time = 0.00962125, size = 47, normalized size = 0.85 \[ c^3 \left (-\frac{a^4}{7 x^7}+\frac{a^3 b}{3 x^6}-\frac{a b^3}{2 x^4}+\frac{b^4}{3 x^3}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x)*(a*c - b*c*x)^3)/x^8,x]
[Out]
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Maple [A] time = 0.007, size = 40, normalized size = 0.7 \[{c}^{3} \left ( -{\frac{{a}^{4}}{7\,{x}^{7}}}+{\frac{{b}^{4}}{3\,{x}^{3}}}-{\frac{a{b}^{3}}{2\,{x}^{4}}}+{\frac{{a}^{3}b}{3\,{x}^{6}}} \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)*(-b*c*x+a*c)^3/x^8,x)
[Out]
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Maxima [A] time = 1.34668, size = 63, normalized size = 1.15 \[ \frac{14 \, b^{4} c^{3} x^{4} - 21 \, a b^{3} c^{3} x^{3} + 14 \, a^{3} b c^{3} x - 6 \, a^{4} c^{3}}{42 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^3*(b*x + a)/x^8,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.196409, size = 63, normalized size = 1.15 \[ \frac{14 \, b^{4} c^{3} x^{4} - 21 \, a b^{3} c^{3} x^{3} + 14 \, a^{3} b c^{3} x - 6 \, a^{4} c^{3}}{42 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^3*(b*x + a)/x^8,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.968414, size = 49, normalized size = 0.89 \[ \frac{- 6 a^{4} c^{3} + 14 a^{3} b c^{3} x - 21 a b^{3} c^{3} x^{3} + 14 b^{4} c^{3} x^{4}}{42 x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)*(-b*c*x+a*c)**3/x**8,x)
[Out]
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GIAC/XCAS [A] time = 0.270836, size = 63, normalized size = 1.15 \[ \frac{14 \, b^{4} c^{3} x^{4} - 21 \, a b^{3} c^{3} x^{3} + 14 \, a^{3} b c^{3} x - 6 \, a^{4} c^{3}}{42 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^3*(b*x + a)/x^8,x, algorithm="giac")
[Out]