3.165 \(\int k^{x^2} x \, dx\)

Optimal. Leaf size=13 \[ \frac{k^{x^2}}{2 \log (k)} \]

[Out]

k^x^2/(2*Log[k])

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Rubi [A]  time = 0.0131667, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143 \[ \frac{k^{x^2}}{2 \log (k)} \]

Antiderivative was successfully verified.

[In]  Int[k^x^2*x,x]

[Out]

k^x^2/(2*Log[k])

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Rubi in Sympy [A]  time = 1.10979, size = 8, normalized size = 0.62 \[ \frac{k^{x^{2}}}{2 \log{\left (k \right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(k**(x**2)*x,x)

[Out]

k**(x**2)/(2*log(k))

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Mathematica [A]  time = 0.00272018, size = 13, normalized size = 1. \[ \frac{k^{x^2}}{2 \log (k)} \]

Antiderivative was successfully verified.

[In]  Integrate[k^x^2*x,x]

[Out]

k^x^2/(2*Log[k])

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Maple [A]  time = 0.002, size = 12, normalized size = 0.9 \[{\frac{{k}^{{x}^{2}}}{2\,\ln \left ( k \right ) }} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(k^(x^2)*x,x)

[Out]

1/2*k^(x^2)/ln(k)

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Maxima [A]  time = 1.41374, size = 15, normalized size = 1.15 \[ \frac{k^{\left (x^{2}\right )}}{2 \, \log \left (k\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(k^(x^2)*x,x, algorithm="maxima")

[Out]

1/2*k^(x^2)/log(k)

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Fricas [A]  time = 0.210551, size = 15, normalized size = 1.15 \[ \frac{k^{\left (x^{2}\right )}}{2 \, \log \left (k\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(k^(x^2)*x,x, algorithm="fricas")

[Out]

1/2*k^(x^2)/log(k)

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Sympy [A]  time = 0.082227, size = 17, normalized size = 1.31 \[ \begin{cases} \frac{k^{x^{2}}}{2 \log{\left (k \right )}} & \text{for}\: 2 \log{\left (k \right )} \neq 0 \\\frac{x^{2}}{2} & \text{otherwise} \end{cases} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(k**(x**2)*x,x)

[Out]

Piecewise((k**(x**2)/(2*log(k)), Ne(2*log(k), 0)), (x**2/2, True))

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GIAC/XCAS [A]  time = 0.19762, size = 15, normalized size = 1.15 \[ \frac{k^{\left (x^{2}\right )}}{2 \,{\rm ln}\left (k\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(k^(x^2)*x,x, algorithm="giac")

[Out]

1/2*k^(x^2)/ln(k)