3.658 \(\int \frac{e^{\sqrt{4+x}}}{\sqrt{4+x}} \, dx\)

Optimal. Leaf size=11 \[ 2 e^{\sqrt{x+4}} \]

[Out]

2*E^Sqrt[4 + x]

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Rubi [A]  time = 0.0237167, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059, Rules used = {2209} \[ 2 e^{\sqrt{x+4}} \]

Antiderivative was successfully verified.

[In]

Int[E^Sqrt[4 + x]/Sqrt[4 + x],x]

[Out]

2*E^Sqrt[4 + x]

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{e^{\sqrt{4+x}}}{\sqrt{4+x}} \, dx &=2 e^{\sqrt{4+x}}\\ \end{align*}

Mathematica [A]  time = 0.0033913, size = 11, normalized size = 1. \[ 2 e^{\sqrt{x+4}} \]

Antiderivative was successfully verified.

[In]

Integrate[E^Sqrt[4 + x]/Sqrt[4 + x],x]

[Out]

2*E^Sqrt[4 + x]

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Maple [A]  time = 0.024, size = 9, normalized size = 0.8 \begin{align*} 2\,{{\rm e}^{\sqrt{4+x}}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp((4+x)^(1/2))/(4+x)^(1/2),x)

[Out]

2*exp((4+x)^(1/2))

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Maxima [A]  time = 0.967904, size = 11, normalized size = 1. \begin{align*} 2 \, e^{\left (\sqrt{x + 4}\right )} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp((4+x)^(1/2))/(4+x)^(1/2),x, algorithm="maxima")

[Out]

2*e^(sqrt(x + 4))

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Fricas [A]  time = 0.678837, size = 26, normalized size = 2.36 \begin{align*} 2 \, e^{\left (\sqrt{x + 4}\right )} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp((4+x)^(1/2))/(4+x)^(1/2),x, algorithm="fricas")

[Out]

2*e^(sqrt(x + 4))

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Sympy [A]  time = 0.193108, size = 8, normalized size = 0.73 \begin{align*} 2 e^{\sqrt{x + 4}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp((4+x)**(1/2))/(4+x)**(1/2),x)

[Out]

2*exp(sqrt(x + 4))

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Giac [A]  time = 1.25851, size = 11, normalized size = 1. \begin{align*} 2 \, e^{\left (\sqrt{x + 4}\right )} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp((4+x)^(1/2))/(4+x)^(1/2),x, algorithm="giac")

[Out]

2*e^(sqrt(x + 4))