Optimal. Leaf size=26 \[ \frac{1}{3} x^3 (-a-b x)^{-n} (a+b x)^n \]
[Out]
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Rubi [A] time = 0.0116704, antiderivative size = 26, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 23, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.087 \[ \frac{1}{3} x^3 (-a-b x)^{-n} (a+b x)^n \]
Antiderivative was successfully verified.
[In] Int[(x^2*(a + b*x)^n)/(-a - b*x)^n,x]
[Out]
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Rubi in Sympy [A] time = 3.7078, size = 19, normalized size = 0.73 \[ \frac{x^{3} \left (- a - b x\right )^{- n} \left (a + b x\right )^{n}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2*(b*x+a)**n/((-b*x-a)**n),x)
[Out]
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Mathematica [A] time = 0.00799606, size = 26, normalized size = 1. \[ \frac{1}{3} x^3 (-a-b x)^{-n} (a+b x)^n \]
Antiderivative was successfully verified.
[In] Integrate[(x^2*(a + b*x)^n)/(-a - b*x)^n,x]
[Out]
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Maple [A] time = 0.003, size = 25, normalized size = 1. \[{\frac{{x}^{3} \left ( bx+a \right ) ^{n}}{3\, \left ( -bx-a \right ) ^{n}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2*(b*x+a)^n/((-b*x-a)^n),x)
[Out]
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Maxima [A] time = 1.35173, size = 14, normalized size = 0.54 \[ \frac{1}{3} \, \left (-1\right )^{-n} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^n*x^2/(-b*x - a)^n,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.242252, size = 12, normalized size = 0.46 \[ \frac{1}{3} \, x^{3} \cos \left (\pi n\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^n*x^2/(-b*x - a)^n,x, algorithm="fricas")
[Out]
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Sympy [A] time = 100.468, size = 19, normalized size = 0.73 \[ \frac{x^{3} \left (- a - b x\right )^{- n} \left (a + b x\right )^{n}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2*(b*x+a)**n/((-b*x-a)**n),x)
[Out]
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GIAC/XCAS [A] time = 0.224543, size = 7, normalized size = 0.27 \[ \frac{1}{3} \, x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^n*x^2/(-b*x - a)^n,x, algorithm="giac")
[Out]