Optimal. Leaf size=16 \[ \frac {x^{2 (1+n)}}{2 (1+n)} \]
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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}
\begin {gather*} \frac {x^{2 (n+1)}}{2 (n+1)} \end {gather*}
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 \begin {gather*} \frac {x^{2+2 n}}{2+2 n} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 16, normalized size = 1.00
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 | \(\frac {x \,{\mathrm e}^{\left (1+2 n \right ) \ln \left (x \right )}}{2+2 n}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 14, normalized size = 0.88 \begin {gather*} \frac {x^{2 \, n + 2}}{2 \, {\left (n + 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 1.13, size = 15, normalized size = 0.94 \begin {gather*} \frac {x x^{2 \, n + 1}}{2 \, {\left (n + 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 15, normalized size = 0.94 \begin {gather*} \begin {cases} \frac {x^{2 n + 2}}{2 n + 2} & \text {for}\: n \neq -1 \\\log {\left (x \right )} & \text {otherwise} \end {cases} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.78, size = 14, normalized size = 0.88 \begin {gather*} \frac {x^{2 \, n + 2}}{2 \, {\left (n + 1\right )}} \end {gather*}
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 \begin {gather*} \left \{\begin {array}{cl} \ln \left (x\right ) & \text {\ if\ \ }n=-1\\ \frac {x^{2\,n+2}}{2\,\left (n+1\right )} & \text {\ if\ \ }n\neq -1 \end {array}\right . \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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