Optimal. Leaf size=57 \[ \frac{4 a^2}{5 b c^6 (a-b x)^5}-\frac{a}{b c^6 (a-b x)^4}+\frac{1}{3 b c^6 (a-b x)^3} \]
[Out]
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Rubi [A] time = 0.0671939, antiderivative size = 57, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.053 \[ \frac{4 a^2}{5 b c^6 (a-b x)^5}-\frac{a}{b c^6 (a-b x)^4}+\frac{1}{3 b c^6 (a-b x)^3} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)^2/(a*c - b*c*x)^6,x]
[Out]
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Rubi in Sympy [A] time = 16.1261, size = 46, normalized size = 0.81 \[ \frac{4 a^{2}}{5 b c^{6} \left (a - b x\right )^{5}} - \frac{a}{b c^{6} \left (a - b x\right )^{4}} + \frac{1}{3 b c^{6} \left (a - b x\right )^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**2/(-b*c*x+a*c)**6,x)
[Out]
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Mathematica [A] time = 0.0303593, size = 38, normalized size = 0.67 \[ -\frac{2 a^2+5 a b x+5 b^2 x^2}{15 b c^6 (b x-a)^5} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)^2/(a*c - b*c*x)^6,x]
[Out]
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Maple [A] time = 0.009, size = 52, normalized size = 0.9 \[{\frac{1}{{c}^{6}} \left ( -{\frac{1}{3\,b \left ( bx-a \right ) ^{3}}}-{\frac{4\,{a}^{2}}{5\,b \left ( bx-a \right ) ^{5}}}-{\frac{a}{b \left ( bx-a \right ) ^{4}}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^2/(-b*c*x+a*c)^6,x)
[Out]
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Maxima [A] time = 1.35367, size = 128, normalized size = 2.25 \[ -\frac{5 \, b^{2} x^{2} + 5 \, a b x + 2 \, a^{2}}{15 \,{\left (b^{6} c^{6} x^{5} - 5 \, a b^{5} c^{6} x^{4} + 10 \, a^{2} b^{4} c^{6} x^{3} - 10 \, a^{3} b^{3} c^{6} x^{2} + 5 \, a^{4} b^{2} c^{6} x - a^{5} b c^{6}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^2/(b*c*x - a*c)^6,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.198223, size = 128, normalized size = 2.25 \[ -\frac{5 \, b^{2} x^{2} + 5 \, a b x + 2 \, a^{2}}{15 \,{\left (b^{6} c^{6} x^{5} - 5 \, a b^{5} c^{6} x^{4} + 10 \, a^{2} b^{4} c^{6} x^{3} - 10 \, a^{3} b^{3} c^{6} x^{2} + 5 \, a^{4} b^{2} c^{6} x - a^{5} b c^{6}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^2/(b*c*x - a*c)^6,x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.49048, size = 100, normalized size = 1.75 \[ - \frac{2 a^{2} + 5 a b x + 5 b^{2} x^{2}}{- 15 a^{5} b c^{6} + 75 a^{4} b^{2} c^{6} x - 150 a^{3} b^{3} c^{6} x^{2} + 150 a^{2} b^{4} c^{6} x^{3} - 75 a b^{5} c^{6} x^{4} + 15 b^{6} c^{6} x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)**2/(-b*c*x+a*c)**6,x)
[Out]
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GIAC/XCAS [A] time = 0.203806, size = 49, normalized size = 0.86 \[ -\frac{5 \, b^{2} x^{2} + 5 \, a b x + 2 \, a^{2}}{15 \,{\left (b x - a\right )}^{5} b c^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^2/(b*c*x - a*c)^6,x, algorithm="giac")
[Out]