3.69 \(\int \frac{2^{\sqrt{x}}}{\sqrt{x}} \, dx\)

Optimal. Leaf size=14 \[ \frac{2^{\sqrt{x}+1}}{\log (2)} \]

[Out]

2^(1 + Sqrt[x])/Log[2]

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Rubi [A]  time = 0.0196678, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{2^{\sqrt{x}+1}}{\log (2)} \]

Antiderivative was successfully verified.

[In]  Int[2^Sqrt[x]/Sqrt[x],x]

[Out]

2^(1 + Sqrt[x])/Log[2]

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Rubi in Sympy [A]  time = 1.32137, size = 10, normalized size = 0.71 \[ \frac{2 \cdot 2^{\sqrt{x}}}{\log{\left (2 \right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(2**(x**(1/2))/x**(1/2),x)

[Out]

2*2**(sqrt(x))/log(2)

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Mathematica [A]  time = 0.00503077, size = 14, normalized size = 1. \[ \frac{2^{\sqrt{x}+1}}{\log (2)} \]

Antiderivative was successfully verified.

[In]  Integrate[2^Sqrt[x]/Sqrt[x],x]

[Out]

2^(1 + Sqrt[x])/Log[2]

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Maple [A]  time = 0.006, size = 12, normalized size = 0.9 \[ 2\,{\frac{{2}^{\sqrt{x}}}{\ln \left ( 2 \right ) }} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(2^(x^(1/2))/x^(1/2),x)

[Out]

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

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Maxima [A]  time = 1.48324, size = 16, normalized size = 1.14 \[ \frac{2^{\sqrt{x} + 1}}{\log \left (2\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(2^sqrt(x)/sqrt(x),x, algorithm="maxima")

[Out]

2^(sqrt(x) + 1)/log(2)

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Fricas [A]  time = 0.207196, size = 15, normalized size = 1.07 \[ \frac{2 \cdot 2^{\left (\sqrt{x}\right )}}{\log \left (2\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(2^sqrt(x)/sqrt(x),x, algorithm="fricas")

[Out]

2*2^sqrt(x)/log(2)

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Sympy [A]  time = 0.152574, size = 10, normalized size = 0.71 \[ \frac{2 \cdot 2^{\sqrt{x}}}{\log{\left (2 \right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(2**(x**(1/2))/x**(1/2),x)

[Out]

2*2**(sqrt(x))/log(2)

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GIAC/XCAS [A]  time = 0.215751, size = 15, normalized size = 1.07 \[ \frac{2 \cdot 2^{\left (\sqrt{x}\right )}}{{\rm ln}\left (2\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(2^sqrt(x)/sqrt(x),x, algorithm="giac")

[Out]

2*2^sqrt(x)/ln(2)