3.1 \(\int x^n \, dx\)

Optimal. Leaf size=11 \[ \frac{x^{n+1}}{n+1} \]

[Out]

x^(1 + n)/(1 + n)

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Rubi [A]  time = 0.00693595, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 3, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.333 \[ \frac{x^{n+1}}{n+1} \]

Antiderivative was successfully verified.

[In]  Int[x^n,x]

[Out]

x^(1 + n)/(1 + n)

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Rubi in Sympy [A]  time = 0.613254, size = 7, normalized size = 0.64 \[ \frac{x^{n + 1}}{n + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**n,x)

[Out]

x**(n + 1)/(n + 1)

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Mathematica [A]  time = 0.00182262, size = 11, normalized size = 1. \[ \frac{x^{n+1}}{n+1} \]

Antiderivative was successfully verified.

[In]  Integrate[x^n,x]

[Out]

x^(1 + n)/(1 + n)

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Maple [A]  time = 0.003, size = 12, normalized size = 1.1 \[{\frac{{x}^{1+n}}{1+n}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^n,x)

[Out]

x^(1+n)/(1+n)

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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(x^n,x, algorithm="maxima")

[Out]

Exception raised: ValueError

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Fricas [A]  time = 0.213276, size = 14, normalized size = 1.27 \[ \frac{x x^{n}}{n + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^n,x, algorithm="fricas")

[Out]

x*x^n/(n + 1)

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Sympy [A]  time = 0.030976, size = 12, normalized size = 1.09 \[ \begin{cases} \frac{x^{n + 1}}{n + 1} & \text{for}\: n \neq -1 \\\log{\left (x \right )} & \text{otherwise} \end{cases} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**n,x)

[Out]

Piecewise((x**(n + 1)/(n + 1), Ne(n, -1)), (log(x), True))

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GIAC/XCAS [A]  time = 0.205615, size = 15, normalized size = 1.36 \[ \frac{x^{n + 1}}{n + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^n,x, algorithm="giac")

[Out]

x^(n + 1)/(n + 1)