Optimal. Leaf size=16 \[ \frac {x^{2 (n+1)}}{2 (n+1)} \]
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Rubi [A] time = 0.00, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {30} \[ \frac {x^{2 (n+1)}}{2 (n+1)} \]
Antiderivative was successfully verified.
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Rule 30
Rubi steps
\begin {align*} \int x^{1+2 n} \, dx &=\frac {x^{2 (1+n)}}{2 (1+n)}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 15, normalized size = 0.94 \[ \frac {x^{2 n+2}}{2 n+2} \]
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int x^{1+2 n} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.86, size = 15, normalized size = 0.94 \[ \frac {x x^{2 \, n + 1}}{2 \, {\left (n + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.58, size = 14, normalized size = 0.88 \[ \frac {x^{2 \, n + 2}}{2 \, {\left (n + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 15, normalized size = 0.94
method | result | size |
gosper | \(\frac {x^{2+2 n}}{2+2 n}\) | \(15\) |
default | \(\frac {x^{2+2 n}}{2+2 n}\) | \(16\) |
risch | \(\frac {x \,x^{1+2 n}}{2+2 n}\) | \(16\) |
norman | \(\frac {x \,{\mathrm e}^{\left (1+2 n \right ) \ln \relax (x )}}{2+2 n}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 14, normalized size = 0.88 \[ \frac {x^{2 \, n + 2}}{2 \, {\left (n + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.46, size = 24, normalized size = 1.50 \[ \left \{\begin {array}{cl} \ln \relax (x) & \text {\ if\ \ }n=-1\\ \frac {x^{2\,n+2}}{2\,\left (n+1\right )} & \text {\ if\ \ }n\neq -1 \end {array}\right . \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 19, normalized size = 1.19 \[ \begin {cases} \frac {x^{2 n + 2}}{2 n + 2} & \text {for}\: 2 n + 1 \neq -1 \\\log {\relax (x )} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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