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

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

[Out]

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

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Rubi [A]  time = 0.01, antiderivative size = 14, normalized size of antiderivative = 1.00, 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*}

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Mathematica [A]  time = 0.00, size = 14, normalized size = 1.00 \[ \frac {2^{\sqrt {x}+1}}{\log (2)} \]

Antiderivative was successfully verified.

[In]

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

[Out]

2^(1 + Sqrt[x])/Log[2]

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fricas [A]  time = 0.41, size = 11, normalized size = 0.79 \[ \frac {2 \cdot 2^{\left (\sqrt {x}\right )}}{\log \relax (2)} \]

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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giac [A]  time = 0.01, size = 11, normalized size = 0.79 \[ \frac {2 \cdot 2^{\left (\sqrt {x}\right )}}{\log \relax (2)} \]

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)

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maple [A]  time = 0.00, size = 12, normalized size = 0.86 \[ \frac {2 \,2^{\sqrt {x}}}{\ln \relax (2)} \]

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 = 0.58, size = 12, normalized size = 0.86 \[ \frac {2^{\sqrt {x} + 1}}{\log \relax (2)} \]

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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mupad [B]  time = 0.10, size = 11, normalized size = 0.79 \[ \frac {2\,2^{\sqrt {x}}}{\ln \relax (2)} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2^(x^(1/2))/x^(1/2),x)

[Out]

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

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sympy [A]  time = 0.18, size = 10, normalized size = 0.71 \[ \frac {2 \cdot 2^{\sqrt {x}}}{\log {\relax (2 )}} \]

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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