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

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 = 0.0105539, 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, Rules used = {2209} \[ \frac{2^{\sqrt{x}+1}}{\log (2)} \]

Antiderivative was successfully verified.

[In]

Int[2^Sqrt[x]/Sqrt[x],x]

[Out]

2^(1 + Sqrt[x])/Log[2]

Rule 2209

Int[(F_)^((a_.) + (b_.)*((c_.) + (d_.)*(x_))^(n_))*((e_.) + (f_.)*(x_))^(m_.), x_Symbol] :> Simp[((e + f*x)^n*
F^(a + b*(c + d*x)^n))/(b*f*n*(c + d*x)^n*Log[F]), x] /; FreeQ[{F, a, b, c, d, e, f, n}, x] && EqQ[m, n - 1] &
& EqQ[d*e - c*f, 0]

Rubi steps

\begin{align*} \int \frac{2^{\sqrt{x}}}{\sqrt{x}} \, dx &=\frac{2^{1+\sqrt{x}}}{\log (2)}\\ \end{align*}

Mathematica [A]  time = 0.002815, 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 = 0.018, size = 12, normalized size = 0.9 \begin{align*} 2\,{\frac{{2}^{\sqrt{x}}}{\ln \left ( 2 \right ) }} \end{align*}

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 = 0.963074, size = 16, normalized size = 1.14 \begin{align*} \frac{2^{\sqrt{x} + 1}}{\log \left (2\right )} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2^(x^(1/2))/x^(1/2),x, algorithm="maxima")

[Out]

2^(sqrt(x) + 1)/log(2)

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Fricas [A]  time = 0.648334, size = 27, normalized size = 1.93 \begin{align*} \frac{2 \cdot 2^{\left (\sqrt{x}\right )}}{\log \left (2\right )} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2^(x^(1/2))/x^(1/2),x, algorithm="fricas")

[Out]

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

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Sympy [A]  time = 0.138863, size = 10, normalized size = 0.71 \begin{align*} \frac{2 \cdot 2^{\sqrt{x}}}{\log{\left (2 \right )}} \end{align*}

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 [A]  time = 1.22954, size = 15, normalized size = 1.07 \begin{align*} \frac{2 \cdot 2^{\left (\sqrt{x}\right )}}{\log \left (2\right )} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2^(x^(1/2))/x^(1/2),x, algorithm="giac")

[Out]

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