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

Optimal. Leaf size=9 \[ 2 e^{\sqrt {x}} \]

[Out]

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

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Rubi [A]
time = 0.01, antiderivative size = 9, 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 = {2240} \begin {gather*} 2 e^{\sqrt {x}} \end {gather*}

Antiderivative was successfully verified.

[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*} \int \frac {e^{\sqrt {x}}}{\sqrt {x}} \, dx &=2 e^{\sqrt {x}}\\ \end {align*}

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Mathematica [A]
time = 0.00, size = 9, normalized size = 1.00 \begin {gather*} 2 e^{\sqrt {x}} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

2*E^Sqrt[x]

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Maple [A]
time = 0.01, size = 7, normalized size = 0.78

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Maxima [A]
time = 0.31, size = 6, normalized size = 0.67 \begin {gather*} 2 \, e^{\sqrt {x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2*e^sqrt(x)

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Fricas [A]
time = 0.36, size = 6, normalized size = 0.67 \begin {gather*} 2 \, e^{\sqrt {x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2*e^sqrt(x)

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Sympy [A]
time = 0.06, size = 7, normalized size = 0.78 \begin {gather*} 2 e^{\sqrt {x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2*exp(sqrt(x))

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Giac [A]
time = 4.76, size = 6, normalized size = 0.67 \begin {gather*} 2 \, e^{\sqrt {x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2*e^sqrt(x)

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Mupad [B]
time = 3.49, size = 6, normalized size = 0.67 \begin {gather*} 2\,{\mathrm {e}}^{\sqrt {x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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