Optimal. Leaf size=21 \[ \frac{a x^3}{3}+\frac{b x^{n+3}}{n+3} \]
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Rubi [A] time = 0.021508, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{a x^3}{3}+\frac{b x^{n+3}}{n+3} \]
Antiderivative was successfully verified.
[In] Int[x^2*(a + b*x^n),x]
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Rubi in Sympy [A] time = 3.6623, size = 15, normalized size = 0.71 \[ \frac{a x^{3}}{3} + \frac{b x^{n + 3}}{n + 3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2*(a+b*x**n),x)
[Out]
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Mathematica [A] time = 0.0163777, size = 21, normalized size = 1. \[ \frac{a x^3}{3}+\frac{b x^{n+3}}{n+3} \]
Antiderivative was successfully verified.
[In] Integrate[x^2*(a + b*x^n),x]
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Maple [A] time = 0.014, size = 23, normalized size = 1.1 \[{\frac{b{x}^{3}{{\rm e}^{n\ln \left ( x \right ) }}}{3+n}}+{\frac{a{x}^{3}}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2*(a+b*x^n),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^n + a)*x^2,x, algorithm="maxima")
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Fricas [A] time = 0.236021, size = 38, normalized size = 1.81 \[ \frac{3 \, b x^{3} x^{n} +{\left (a n + 3 \, a\right )} x^{3}}{3 \,{\left (n + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^n + a)*x^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.02459, size = 51, normalized size = 2.43 \[ \begin{cases} \frac{a n x^{3}}{3 n + 9} + \frac{3 a x^{3}}{3 n + 9} + \frac{3 b x^{3} x^{n}}{3 n + 9} & \text{for}\: n \neq -3 \\\frac{a x^{3}}{3} + b \log{\left (x \right )} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2*(a+b*x**n),x)
[Out]
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GIAC/XCAS [A] time = 0.212706, size = 42, normalized size = 2. \[ \frac{a n x^{3} + 3 \, b x^{3} e^{\left (n{\rm ln}\left (x\right )\right )} + 3 \, a x^{3}}{3 \,{\left (n + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^n + a)*x^2,x, algorithm="giac")
[Out]