Optimal. Leaf size=17 \[ -\frac{1}{2 b c^8 (a+b x)^2} \]
[Out]
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Rubi [A] time = 0.0122736, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ -\frac{1}{2 b c^8 (a+b x)^2} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)^5/(a*c + b*c*x)^8,x]
[Out]
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Rubi in Sympy [A] time = 4.1028, size = 15, normalized size = 0.88 \[ - \frac{1}{2 b c^{8} \left (a + b x\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**5/(b*c*x+a*c)**8,x)
[Out]
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Mathematica [A] time = 0.00597728, size = 17, normalized size = 1. \[ -\frac{1}{2 b c^8 (a+b x)^2} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)^5/(a*c + b*c*x)^8,x]
[Out]
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Maple [A] time = 0.002, size = 16, normalized size = 0.9 \[ -{\frac{1}{2\,b{c}^{8} \left ( bx+a \right ) ^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^5/(b*c*x+a*c)^8,x)
[Out]
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Maxima [A] time = 1.33122, size = 45, normalized size = 2.65 \[ -\frac{1}{2 \,{\left (b^{3} c^{8} x^{2} + 2 \, a b^{2} c^{8} x + a^{2} b c^{8}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^5/(b*c*x + a*c)^8,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.190956, size = 45, normalized size = 2.65 \[ -\frac{1}{2 \,{\left (b^{3} c^{8} x^{2} + 2 \, a b^{2} c^{8} x + a^{2} b c^{8}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^5/(b*c*x + a*c)^8,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.555, size = 36, normalized size = 2.12 \[ - \frac{1}{2 a^{2} b c^{8} + 4 a b^{2} c^{8} x + 2 b^{3} c^{8} x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)**5/(b*c*x+a*c)**8,x)
[Out]
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GIAC/XCAS [A] time = 0.208155, size = 20, normalized size = 1.18 \[ -\frac{1}{2 \,{\left (b x + a\right )}^{2} b c^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^5/(b*c*x + a*c)^8,x, algorithm="giac")
[Out]