Optimal. Leaf size=41 \[ -\frac{c^5 (a-b x)^6}{7 x^7}-\frac{4 b c^5 (a-b x)^6}{21 a x^6} \]
[Out]
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Rubi [A] time = 0.0483606, antiderivative size = 41, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1 \[ -\frac{c^5 (a-b x)^6}{7 x^7}-\frac{4 b c^5 (a-b x)^6}{21 a x^6} \]
Antiderivative was successfully verified.
[In] Int[((a + b*x)*(a*c - b*c*x)^5)/x^8,x]
[Out]
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Rubi in Sympy [A] time = 11.6774, size = 36, normalized size = 0.88 \[ - \frac{c^{5} \left (a - b x\right )^{6}}{7 x^{7}} - \frac{4 b c^{5} \left (a - b x\right )^{6}}{21 a x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)*(-b*c*x+a*c)**5/x**8,x)
[Out]
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Mathematica [A] time = 0.0114612, size = 66, normalized size = 1.61 \[ c^5 \left (-\frac{a^6}{7 x^7}+\frac{2 a^5 b}{3 x^6}-\frac{a^4 b^2}{x^5}+\frac{5 a^2 b^4}{3 x^3}-\frac{2 a b^5}{x^2}+\frac{b^6}{x}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x)*(a*c - b*c*x)^5)/x^8,x]
[Out]
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Maple [A] time = 0.008, size = 61, normalized size = 1.5 \[{c}^{5} \left ( -{\frac{{a}^{6}}{7\,{x}^{7}}}-2\,{\frac{a{b}^{5}}{{x}^{2}}}-{\frac{{a}^{4}{b}^{2}}{{x}^{5}}}+{\frac{{b}^{6}}{x}}+{\frac{5\,{a}^{2}{b}^{4}}{3\,{x}^{3}}}+{\frac{2\,{a}^{5}b}{3\,{x}^{6}}} \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)*(-b*c*x+a*c)^5/x^8,x)
[Out]
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Maxima [A] time = 1.35168, size = 101, normalized size = 2.46 \[ \frac{21 \, b^{6} c^{5} x^{6} - 42 \, a b^{5} c^{5} x^{5} + 35 \, a^{2} b^{4} c^{5} x^{4} - 21 \, a^{4} b^{2} c^{5} x^{2} + 14 \, a^{5} b c^{5} x - 3 \, a^{6} c^{5}}{21 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^5*(b*x + a)/x^8,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.200362, size = 101, normalized size = 2.46 \[ \frac{21 \, b^{6} c^{5} x^{6} - 42 \, a b^{5} c^{5} x^{5} + 35 \, a^{2} b^{4} c^{5} x^{4} - 21 \, a^{4} b^{2} c^{5} x^{2} + 14 \, a^{5} b c^{5} x - 3 \, a^{6} c^{5}}{21 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^5*(b*x + a)/x^8,x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.56319, size = 80, normalized size = 1.95 \[ \frac{- 3 a^{6} c^{5} + 14 a^{5} b c^{5} x - 21 a^{4} b^{2} c^{5} x^{2} + 35 a^{2} b^{4} c^{5} x^{4} - 42 a b^{5} c^{5} x^{5} + 21 b^{6} c^{5} x^{6}}{21 x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)*(-b*c*x+a*c)**5/x**8,x)
[Out]
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GIAC/XCAS [A] time = 0.25478, size = 101, normalized size = 2.46 \[ \frac{21 \, b^{6} c^{5} x^{6} - 42 \, a b^{5} c^{5} x^{5} + 35 \, a^{2} b^{4} c^{5} x^{4} - 21 \, a^{4} b^{2} c^{5} x^{2} + 14 \, a^{5} b c^{5} x - 3 \, a^{6} c^{5}}{21 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^5*(b*x + a)/x^8,x, algorithm="giac")
[Out]