Optimal. Leaf size=33 \[ \frac{2 k^{x/2}}{\log (k)}+\frac{x^{\sqrt{k}+1}}{\sqrt{k}+1} \]
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Rubi [A] time = 0.0188467, antiderivative size = 33, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ \frac{2 k^{x/2}}{\log (k)}+\frac{x^{\sqrt{k}+1}}{\sqrt{k}+1} \]
Antiderivative was successfully verified.
[In] Int[k^(x/2) + x^Sqrt[k],x]
[Out]
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Rubi in Sympy [A] time = 1.57341, size = 24, normalized size = 0.73 \[ \frac{2 k^{\frac{x}{2}}}{\log{\left (k \right )}} + \frac{x^{\sqrt{k} + 1}}{\sqrt{k} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(k**(1/2*x)+x**(k**(1/2)),x)
[Out]
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Mathematica [A] time = 0.0233965, size = 33, normalized size = 1. \[ \frac{2 k^{x/2}}{\log (k)}+\frac{x^{\sqrt{k}+1}}{\sqrt{k}+1} \]
Antiderivative was successfully verified.
[In] Integrate[k^(x/2) + x^Sqrt[k],x]
[Out]
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Maple [A] time = 0.003, size = 28, normalized size = 0.9 \[ 2\,{\frac{{k}^{x/2}}{\ln \left ( k \right ) }}+{1{x}^{1+\sqrt{k}} \left ( 1+\sqrt{k} \right ) ^{-1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(k^(1/2*x)+x^(k^(1/2)),x)
[Out]
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Maxima [A] time = 0.774473, size = 36, normalized size = 1.09 \[ \frac{x^{\sqrt{k} + 1}}{\sqrt{k} + 1} + \frac{2 \, k^{\frac{1}{2} \, x}}{\log \left (k\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(k^(1/2*x) + x^sqrt(k),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.317117, size = 46, normalized size = 1.39 \[ \frac{x x^{\left (\sqrt{k}\right )} \log \left (k\right ) + 2 \, k^{\frac{1}{2} \, x}{\left (\sqrt{k} + 1\right )}}{\sqrt{k} \log \left (k\right ) + \log \left (k\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(k^(1/2*x) + x^sqrt(k),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.086396, size = 36, normalized size = 1.09 \[ \begin{cases} \frac{2 k^{\frac{x}{2}}}{\log{\left (k \right )}} & \text{for}\: \log{\left (k \right )} \neq 0 \\x & \text{otherwise} \end{cases} + \begin{cases} \frac{x^{\sqrt{k} + 1}}{\sqrt{k} + 1} & \text{for}\: \sqrt{k} \neq -1 \\\log{\left (x \right )} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(k**(1/2*x)+x**(k**(1/2)),x)
[Out]
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GIAC/XCAS [A] time = 0.225033, size = 36, normalized size = 1.09 \[ \frac{x^{\sqrt{k} + 1}}{\sqrt{k} + 1} + \frac{2 \, k^{\frac{1}{2} \, x}}{{\rm ln}\left (k\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(k^(1/2*x) + x^sqrt(k),x, algorithm="giac")
[Out]