\(\int \frac {1}{10} (4+5 e) \, dx\) [7641]

Optimal result

Integrand size = 9, antiderivative size = 27 \[ \int \frac {1}{10} (4+5 e) \, dx=1+\frac {1}{2} \left (-4 \left (-3 e^3-\frac {x}{5}\right )+e \left (e^4+x\right )\right ) \]

[Out]

1+1/2*(exp(2)^2+x)*exp(1)+2/5*x+6*exp(3)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.37, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {8} \[ \int \frac {1}{10} (4+5 e) \, dx=\frac {1}{10} (4+5 e) x \]

[In]

Int[(4 + 5*E)/10,x]

[Out]

((4 + 5*E)*x)/10

Rule 8

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

Rubi steps \begin{align*} \text {integral}& = \frac {1}{10} (4+5 e) x \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.44 \[ \int \frac {1}{10} (4+5 e) \, dx=\frac {2 x}{5}+\frac {e x}{2} \]

[In]

Integrate[(4 + 5*E)/10,x]

[Out]

(2*x)/5 + (E*x)/2

Maple [A] (verified)

Time = 0.01 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.33

method	result	size
norman	\(\left (\frac {{\mathrm e}}{2}+\frac {2}{5}\right ) x\)	\(9\)
parallelrisch	\(\left (\frac {{\mathrm e}}{2}+\frac {2}{5}\right ) x\)	\(9\)
default	\(\frac {x \left (5 \,{\mathrm e}+4\right )}{10}\)	\(10\)
risch	\(\frac {x \,{\mathrm e}}{2}+\frac {2 x}{5}\)	\(10\)
parts	\(\frac {x \,{\mathrm e}}{2}+\frac {2 x}{5}\)	\(10\)

[In]

int(1/2*exp(1)+2/5,x,method=_RETURNVERBOSE)

[Out]

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

Fricas [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.33 \[ \int \frac {1}{10} (4+5 e) \, dx=\frac {1}{2} \, x e + \frac {2}{5} \, x \]

[In]

integrate(1/2*exp(1)+2/5,x, algorithm="fricas")

[Out]

1/2*x*e + 2/5*x

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.30 \[ \int \frac {1}{10} (4+5 e) \, dx=x \left (\frac {2}{5} + \frac {e}{2}\right ) \]

[In]

integrate(1/2*exp(1)+2/5,x)

[Out]

x*(2/5 + E/2)

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.33 \[ \int \frac {1}{10} (4+5 e) \, dx=\frac {1}{10} \, x {\left (5 \, e + 4\right )} \]

[In]

integrate(1/2*exp(1)+2/5,x, algorithm="maxima")

[Out]

1/10*x*(5*e + 4)

Giac [A] (verification not implemented)

none

Time = 0.31 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.33 \[ \int \frac {1}{10} (4+5 e) \, dx=\frac {1}{10} \, x {\left (5 \, e + 4\right )} \]

[In]

integrate(1/2*exp(1)+2/5,x, algorithm="giac")

[Out]

1/10*x*(5*e + 4)

Mupad [B] (verification not implemented)

Time = 0.00 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.30 \[ \int \frac {1}{10} (4+5 e) \, dx=x\,\left (\frac {\mathrm {e}}{2}+\frac {2}{5}\right ) \]

[In]

int(exp(1)/2 + 2/5,x)

[Out]

x*(exp(1)/2 + 2/5)