\(\int \frac {2^{\sqrt {x}}}{\sqrt {x}} \, dx\) [69]

Optimal result

Integrand size = 13, antiderivative size = 14 \[ \int \frac {2^{\sqrt {x}}}{\sqrt {x}} \, dx=\frac {2^{1+\sqrt {x}}}{\log (2)} \]

[Out]

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

Rubi [A] (verified)

Time = 0.01 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {2240} \[ \int \frac {2^{\sqrt {x}}}{\sqrt {x}} \, dx=\frac {2^{\sqrt {x}+1}}{\log (2)} \]

[In]

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

[Out]

2^(1 + Sqrt[x])/Log[2]

Rule 2240

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*} \text {integral}& = \frac {2^{1+\sqrt {x}}}{\log (2)} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00 \[ \int \frac {2^{\sqrt {x}}}{\sqrt {x}} \, dx=\frac {2^{1+\sqrt {x}}}{\log (2)} \]

[In]

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

[Out]

2^(1 + Sqrt[x])/Log[2]

Maple [A] (verified)

Time = 0.05 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86

method	result	size
derivativedivides	\(\frac {2 \,2^{\sqrt {x}}}{\ln \left (2\right )}\)	\(12\)
default	\(\frac {2 \,2^{\sqrt {x}}}{\ln \left (2\right )}\)	\(12\)
meijerg	\(-\frac {2 \left (1-{\mathrm e}^{\sqrt {x}\, \ln \left (2\right )}\right )}{\ln \left (2\right )}\)	\(18\)

[In]

int(2^(x^(1/2))/x^(1/2),x,method=_RETURNVERBOSE)

[Out]

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

Fricas [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.79 \[ \int \frac {2^{\sqrt {x}}}{\sqrt {x}} \, dx=\frac {2 \cdot 2^{\left (\sqrt {x}\right )}}{\log \left (2\right )} \]

[In]

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

[Out]

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

Sympy [A] (verification not implemented)

Time = 0.07 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.71 \[ \int \frac {2^{\sqrt {x}}}{\sqrt {x}} \, dx=\frac {2 \cdot 2^{\sqrt {x}}}{\log {\left (2 \right )}} \]

[In]

integrate(2**(x**(1/2))/x**(1/2),x)

[Out]

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

Maxima [A] (verification not implemented)

none

Time = 0.17 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86 \[ \int \frac {2^{\sqrt {x}}}{\sqrt {x}} \, dx=\frac {2^{\sqrt {x} + 1}}{\log \left (2\right )} \]

[In]

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

[Out]

2^(sqrt(x) + 1)/log(2)

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.79 \[ \int \frac {2^{\sqrt {x}}}{\sqrt {x}} \, dx=\frac {2 \cdot 2^{\left (\sqrt {x}\right )}}{\log \left (2\right )} \]

[In]

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

[Out]

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

Mupad [B] (verification not implemented)

Time = 0.12 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.79 \[ \int \frac {2^{\sqrt {x}}}{\sqrt {x}} \, dx=\frac {2\,2^{\sqrt {x}}}{\ln \left (2\right )} \]

[In]

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

[Out]

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