Optimal. Leaf size=21 \[ \frac{a x^2}{2}+\frac{b x^{n+2}}{n+2} \]
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Rubi [A] time = 0.023482, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ \frac{a x^2}{2}+\frac{b x^{n+2}}{n+2} \]
Antiderivative was successfully verified.
[In] Int[x*(a + b*x^n),x]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ a \int x\, dx + \frac{b x^{n + 2}}{n + 2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*(a+b*x**n),x)
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Mathematica [A] time = 0.0158452, size = 21, normalized size = 1. \[ \frac{a x^2}{2}+\frac{b x^{n+2}}{n+2} \]
Antiderivative was successfully verified.
[In] Integrate[x*(a + b*x^n),x]
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Maple [A] time = 0.012, size = 23, normalized size = 1.1 \[{\frac{b{x}^{2}{{\rm e}^{n\ln \left ( x \right ) }}}{2+n}}+{\frac{a{x}^{2}}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*(a+b*x^n),x)
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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,x, algorithm="maxima")
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Fricas [A] time = 0.237998, size = 38, normalized size = 1.81 \[ \frac{2 \, b x^{2} x^{n} +{\left (a n + 2 \, a\right )} x^{2}}{2 \,{\left (n + 2\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^n + a)*x,x, algorithm="fricas")
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Sympy [A] time = 0.713776, size = 51, normalized size = 2.43 \[ \begin{cases} \frac{a n x^{2}}{2 n + 4} + \frac{2 a x^{2}}{2 n + 4} + \frac{2 b x^{2} x^{n}}{2 n + 4} & \text{for}\: n \neq -2 \\\frac{a x^{2}}{2} + b \log{\left (x \right )} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*(a+b*x**n),x)
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GIAC/XCAS [A] time = 0.213672, size = 42, normalized size = 2. \[ \frac{a n x^{2} + 2 \, b x^{2} e^{\left (n{\rm ln}\left (x\right )\right )} + 2 \, a x^{2}}{2 \,{\left (n + 2\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^n + a)*x,x, algorithm="giac")
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