\(\int \frac {e^{\sqrt {4+x}}}{\sqrt {4+x}} \, dx\) [658]

Optimal result

Integrand size = 17, antiderivative size = 11 \[ \int \frac {e^{\sqrt {4+x}}}{\sqrt {4+x}} \, dx=2 e^{\sqrt {4+x}} \]

[Out]

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

Rubi [A] (verified)

Time = 0.02 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {2240} \[ \int \frac {e^{\sqrt {4+x}}}{\sqrt {4+x}} \, dx=2 e^{\sqrt {x+4}} \]

[In]

Int[E^Sqrt[4 + x]/Sqrt[4 + x],x]

[Out]

2*E^Sqrt[4 + 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 {4+x}} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00 \[ \int \frac {e^{\sqrt {4+x}}}{\sqrt {4+x}} \, dx=2 e^{\sqrt {4+x}} \]

[In]

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

[Out]

2*E^Sqrt[4 + x]

Maple [A] (verified)

Time = 0.32 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.82

method	result	size
derivativedivides	\(2 \,{\mathrm e}^{\sqrt {4+x}}\)	\(9\)
default	\(2 \,{\mathrm e}^{\sqrt {4+x}}\)	\(9\)

[In]

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

[Out]

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

Fricas [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.73 \[ \int \frac {e^{\sqrt {4+x}}}{\sqrt {4+x}} \, dx=2 \, e^{\left (\sqrt {x + 4}\right )} \]

[In]

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

[Out]

2*e^(sqrt(x + 4))

Sympy [A] (verification not implemented)

Time = 0.09 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.73 \[ \int \frac {e^{\sqrt {4+x}}}{\sqrt {4+x}} \, dx=2 e^{\sqrt {x + 4}} \]

[In]

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

[Out]

2*exp(sqrt(x + 4))

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.73 \[ \int \frac {e^{\sqrt {4+x}}}{\sqrt {4+x}} \, dx=2 \, e^{\left (\sqrt {x + 4}\right )} \]

[In]

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

[Out]

2*e^(sqrt(x + 4))

Giac [A] (verification not implemented)

none

Time = 0.30 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.73 \[ \int \frac {e^{\sqrt {4+x}}}{\sqrt {4+x}} \, dx=2 \, e^{\left (\sqrt {x + 4}\right )} \]

[In]

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

[Out]

2*e^(sqrt(x + 4))

Mupad [B] (verification not implemented)

Time = 0.36 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.73 \[ \int \frac {e^{\sqrt {4+x}}}{\sqrt {4+x}} \, dx=2\,{\mathrm {e}}^{\sqrt {x+4}} \]

[In]

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

[Out]

2*exp((x + 4)^(1/2))