Optimal. Leaf size=10 \[ \frac{x}{(a-b x)^2} \]
[Out]
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Rubi [A] time = 0.0187644, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{x}{(a-b x)^2} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)^4/(a^2 - b^2*x^2)^3,x]
[Out]
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Rubi in Sympy [A] time = 6.80813, size = 17, normalized size = 1.7 \[ \frac{\left (a + b x\right )^{2}}{4 a b \left (a - b x\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**4/(-b**2*x**2+a**2)**3,x)
[Out]
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Mathematica [A] time = 0.00647806, size = 10, normalized size = 1. \[ \frac{x}{(a-b x)^2} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)^4/(a^2 - b^2*x^2)^3,x]
[Out]
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Maple [B] time = 0.006, size = 29, normalized size = 2.9 \[{\frac{1}{b \left ( bx-a \right ) }}+{\frac{a}{b \left ( bx-a \right ) ^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^4/(-b^2*x^2+a^2)^3,x)
[Out]
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Maxima [A] time = 0.681401, size = 27, normalized size = 2.7 \[ \frac{x}{b^{2} x^{2} - 2 \, a b x + a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*x + a)^4/(b^2*x^2 - a^2)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.207338, size = 27, normalized size = 2.7 \[ \frac{x}{b^{2} x^{2} - 2 \, a b x + a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*x + a)^4/(b^2*x^2 - a^2)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.46793, size = 17, normalized size = 1.7 \[ \frac{x}{a^{2} - 2 a b x + b^{2} x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)**4/(-b**2*x**2+a**2)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.214285, size = 15, normalized size = 1.5 \[ \frac{x}{{\left (b x - a\right )}^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*x + a)^4/(b^2*x^2 - a^2)^3,x, algorithm="giac")
[Out]