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

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

[Out]

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

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Rubi [A]  time = 0.02, antiderivative size = 11, normalized size of antiderivative = 1.00, 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*}

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Mathematica [A]  time = 0.00, size = 11, normalized size = 1.00 \[ 2 e^{\sqrt {x+4}} \]

Antiderivative was successfully verified.

[In]

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

[Out]

2*E^Sqrt[4 + x]

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fricas [A]  time = 0.40, size = 8, normalized size = 0.73 \[ 2 \, e^{\left (\sqrt {x + 4}\right )} \]

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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giac [A]  time = 0.20, size = 8, normalized size = 0.73 \[ 2 \, e^{\left (\sqrt {x + 4}\right )} \]

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))

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maple [A]  time = 0.02, size = 9, normalized size = 0.82 \[ 2 \,{\mathrm e}^{\sqrt {x +4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.88, size = 8, normalized size = 0.73 \[ 2 \, e^{\left (\sqrt {x + 4}\right )} \]

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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mupad [B]  time = 3.46, size = 8, normalized size = 0.73 \[ 2\,{\mathrm {e}}^{\sqrt {x+4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2*exp((x + 4)^(1/2))

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sympy [A]  time = 0.21, size = 8, normalized size = 0.73 \[ 2 e^{\sqrt {x + 4}} \]

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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