Optimal. Leaf size=11 \[ \frac{x^{n+1}}{n+1} \]
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Rubi [A] time = 0.0023506, 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, Rules used = {30} \[ \frac{x^{n+1}}{n+1} \]
Antiderivative was successfully verified.
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Rule 30
Rubi steps
\begin{align*} \int x^n \, dx &=\frac{x^{1+n}}{1+n}\\ \end{align*}
Mathematica [A] time = 0.0014014, size = 11, normalized size = 1. \[ \frac{x^{n+1}}{n+1} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 12, normalized size = 1.1 \begin{align*}{\frac{{x}^{1+n}}{1+n}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: ValueError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.89629, size = 20, normalized size = 1.82 \begin{align*} \frac{x x^{n}}{n + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.053293, size = 12, normalized size = 1.09 \begin{align*} \begin{cases} \frac{x^{n + 1}}{n + 1} & \text{for}\: n \neq -1 \\\log{\left (x \right )} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.0705, size = 15, normalized size = 1.36 \begin{align*} \frac{x^{n + 1}}{n + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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