\(\int \frac {e^{\sqrt {x}}}{\sqrt {x}} \, dx\) [671]

Optimal result

Integrand size = 13, antiderivative size = 9 \[ \int \frac {e^{\sqrt {x}}}{\sqrt {x}} \, dx=2 e^{\sqrt {x}} \]

[Out]

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

Rubi [A] (verified)

Time = 0.01 (sec) , antiderivative size = 9, 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} \[ \int \frac {e^{\sqrt {x}}}{\sqrt {x}} \, dx=2 e^{\sqrt {x}} \]

[In]

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

[Out]

2*E^Sqrt[x]

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}& = 2 e^{\sqrt {x}} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.00 \[ \int \frac {e^{\sqrt {x}}}{\sqrt {x}} \, dx=2 e^{\sqrt {x}} \]

[In]

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

[Out]

2*E^Sqrt[x]

Maple [A] (verified)

Time = 0.02 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.78

method	result	size
derivativedivides	\(2 \,{\mathrm e}^{\sqrt {x}}\)	\(7\)
default	\(2 \,{\mathrm e}^{\sqrt {x}}\)	\(7\)
meijerg	\(-2+2 \,{\mathrm e}^{\sqrt {x}}\)	\(9\)

[In]

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

[Out]

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

Fricas [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.67 \[ \int \frac {e^{\sqrt {x}}}{\sqrt {x}} \, dx=2 \, e^{\sqrt {x}} \]

[In]

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

[Out]

2*e^sqrt(x)

Sympy [A] (verification not implemented)

Time = 0.08 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.78 \[ \int \frac {e^{\sqrt {x}}}{\sqrt {x}} \, dx=2 e^{\sqrt {x}} \]

[In]

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

[Out]

2*exp(sqrt(x))

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.67 \[ \int \frac {e^{\sqrt {x}}}{\sqrt {x}} \, dx=2 \, e^{\sqrt {x}} \]

[In]

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

[Out]

2*e^sqrt(x)

Giac [A] (verification not implemented)

none

Time = 0.30 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.67 \[ \int \frac {e^{\sqrt {x}}}{\sqrt {x}} \, dx=2 \, e^{\sqrt {x}} \]

[In]

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

[Out]

2*e^sqrt(x)

Mupad [B] (verification not implemented)

Time = 0.26 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.67 \[ \int \frac {e^{\sqrt {x}}}{\sqrt {x}} \, dx=2\,{\mathrm {e}}^{\sqrt {x}} \]

[In]

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

[Out]

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