Optimal. Leaf size=16 \[ a x+\frac{b x^{n+1}}{n+1} \]
[Out]
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Rubi [A] time = 0.0156328, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ a x+\frac{b x^{n+1}}{n+1} \]
Antiderivative was successfully verified.
[In] Int[a + b*x^n,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{b x^{n + 1}}{n + 1} + \int a\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(a+b*x**n,x)
[Out]
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Mathematica [A] time = 0.00938126, size = 16, normalized size = 1. \[ a x+\frac{b x^{n+1}}{n+1} \]
Antiderivative was successfully verified.
[In] Integrate[a + b*x^n,x]
[Out]
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Maple [A] time = 0.002, size = 17, normalized size = 1.1 \[ ax+{\frac{b{x}^{1+n}}{1+n}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(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, algorithm="maxima")
[Out]
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Fricas [A] time = 0.237069, size = 27, normalized size = 1.69 \[ \frac{b x x^{n} +{\left (a n + a\right )} x}{n + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(b*x^n + a,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.065156, size = 17, normalized size = 1.06 \[ a x + b \left (\begin{cases} \frac{x^{n + 1}}{n + 1} & \text{for}\: n \neq -1 \\\log{\left (x \right )} & \text{otherwise} \end{cases}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(a+b*x**n,x)
[Out]
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GIAC/XCAS [A] time = 0.210342, size = 22, normalized size = 1.38 \[ a x + \frac{b x^{n + 1}}{n + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(b*x^n + a,x, algorithm="giac")
[Out]