Optimal. Leaf size=13 \[ \frac {k^{x^2}}{2 \log (k)} \]
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Rubi [A] time = 0.01, antiderivative size = 13, 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 = {2209} \[ \frac {k^{x^2}}{2 \log (k)} \]
Antiderivative was successfully verified.
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Rule 2209
Rubi steps
\begin {align*} \int k^{x^2} x \, dx &=\frac {k^{x^2}}{2 \log (k)}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 13, normalized size = 1.00 \[ \frac {k^{x^2}}{2 \log (k)} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 11, normalized size = 0.85 \[ \frac {k^{\left (x^{2}\right )}}{2 \, \log \relax (k)} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.05, size = 11, normalized size = 0.85 \[ \frac {k^{\left (x^{2}\right )}}{2 \, \log \relax (k)} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 12, normalized size = 0.92 \[ \frac {k^{x^{2}}}{2 \ln \relax (k )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.43, size = 11, normalized size = 0.85 \[ \frac {k^{\left (x^{2}\right )}}{2 \, \log \relax (k)} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 11, normalized size = 0.85 \[ \frac {k^{x^2}}{2\,\ln \relax (k)} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 17, normalized size = 1.31 \[ \begin {cases} \frac {k^{x^{2}}}{2 \log {\relax (k )}} & \text {for}\: 2 \log {\relax (k )} \neq 0 \\\frac {x^{2}}{2} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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