\(\int (5+e) \, dx\) [6826]

Optimal result

Integrand size = 3, antiderivative size = 18 \[ \int (5+e) \, dx=x \left (5+e-\frac {\log \left (5 e^{e^2}\right )}{x}\right ) \]

[Out]

(5-ln(5*exp(exp(2)))/x+exp(1))*x

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.28, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.333, Rules used = {8} \[ \int (5+e) \, dx=(5+e) x \]

[In]

Int[5 + E,x]

[Out]

(5 + E)*x

Rule 8

Int[a_, x_Symbol] :> Simp[a*x, x] /; FreeQ[a, x]

Rubi steps \begin{align*} \text {integral}& = (5+e) x \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.39 \[ \int (5+e) \, dx=5 x+e x \]

[In]

Integrate[5 + E,x]

[Out]

5*x + E*x

Maple [A] (verified)

Time = 0.02 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.39

method	result	size
default	\(x \left ({\mathrm e}+5\right )\)	\(7\)
norman	\(x \left ({\mathrm e}+5\right )\)	\(7\)
parallelrisch	\(x \left ({\mathrm e}+5\right )\)	\(7\)
risch	\(x \,{\mathrm e}+5 x\)	\(9\)
parts	\(x \,{\mathrm e}+5 x\)	\(9\)

[In]

int(exp(1)+5,x,method=_RETURNVERBOSE)

[Out]

x*(exp(1)+5)

Fricas [A] (verification not implemented)

none

Time = 0.23 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.44 \[ \int (5+e) \, dx=x e + 5 \, x \]

[In]

integrate(exp(1)+5,x, algorithm="fricas")

[Out]

x*e + 5*x

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.28 \[ \int (5+e) \, dx=x \left (e + 5\right ) \]

[In]

integrate(exp(1)+5,x)

[Out]

x*(E + 5)

Maxima [A] (verification not implemented)

none

Time = 0.18 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.33 \[ \int (5+e) \, dx=x {\left (e + 5\right )} \]

[In]

integrate(exp(1)+5,x, algorithm="maxima")

[Out]

x*(e + 5)

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.33 \[ \int (5+e) \, dx=x {\left (e + 5\right )} \]

[In]

integrate(exp(1)+5,x, algorithm="giac")

[Out]

x*(e + 5)

Mupad [B] (verification not implemented)

Time = 0.00 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.33 \[ \int (5+e) \, dx=x\,\left (\mathrm {e}+5\right ) \]

[In]

int(exp(1) + 5,x)

[Out]

x*(exp(1) + 5)