Optimal. Leaf size=37 \[ -\frac {x^{m+1} \left (-x^n\right )^{-\frac {m+1}{n}} \Gamma \left (\frac {m+1}{n},-x^n\right )}{n} \]
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Rubi [A] time = 0.02, antiderivative size = 37, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {2218} \[ -\frac {x^{m+1} \left (-x^n\right )^{-\frac {m+1}{n}} \text {Gamma}\left (\frac {m+1}{n},-x^n\right )}{n} \]
Antiderivative was successfully verified.
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Rule 2218
Rubi steps
\begin {align*} \int e^{x^n} x^m \, dx &=-\frac {x^{1+m} \left (-x^n\right )^{-\frac {1+m}{n}} \Gamma \left (\frac {1+m}{n},-x^n\right )}{n}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 37, normalized size = 1.00 \[ -\frac {x^{m+1} \left (-x^n\right )^{-\frac {m+1}{n}} \Gamma \left (\frac {m+1}{n},-x^n\right )}{n} \]
Antiderivative was successfully verified.
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fricas [F] time = 0.41, size = 0, normalized size = 0.00 \[ {\rm integral}\left (x^{m} e^{\left (x^{n}\right )}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int x^{m} e^{\left (x^{n}\right )}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.10, size = 0, normalized size = 0.00 \[ \int x^{m} {\mathrm e}^{x^{n}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.98, size = 38, normalized size = 1.03 \[ -\frac {x^{m + 1} \Gamma \left (\frac {m + 1}{n}, -x^{n}\right )}{n \left (-x^{n}\right )^{\frac {m + 1}{n}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.75, size = 58, normalized size = 1.57 \[ \frac {x^{m+1}\,{\mathrm {e}}^{\frac {x^n}{2}}\,{\mathrm {M}}_{1-\frac {m+n+1}{2\,n},\frac {m+n+1}{2\,n}-\frac {1}{2}}\left (x^n\right )}{{\left (x^n\right )}^{\frac {m+n+1}{2\,n}}\,\left (m+1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [C] time = 1.38, size = 105, normalized size = 2.84 \[ \frac {m e^{- \frac {i \pi }{n}} e^{- \frac {i \pi m}{n}} \Gamma \left (\frac {m}{n} + \frac {1}{n}\right ) \gamma \left (\frac {m}{n} + \frac {1}{n}, x^{n} e^{i \pi }\right )}{n^{2} \Gamma \left (\frac {m}{n} + 1 + \frac {1}{n}\right )} + \frac {e^{- \frac {i \pi }{n}} e^{- \frac {i \pi m}{n}} \Gamma \left (\frac {m}{n} + \frac {1}{n}\right ) \gamma \left (\frac {m}{n} + \frac {1}{n}, x^{n} e^{i \pi }\right )}{n^{2} \Gamma \left (\frac {m}{n} + 1 + \frac {1}{n}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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