\(\int \frac {1}{30} (6+e^{10}) \, dx\) [4830]

Optimal result

Integrand size = 9, antiderivative size = 15 \[ \int \frac {1}{30} \left (6+e^{10}\right ) \, dx=\frac {1}{5} \left (1+x+\frac {e^{10} x}{6}\right ) \]

[Out]

1/30*x*exp(10)+1/5*x+1/5

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.67, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {8} \[ \int \frac {1}{30} \left (6+e^{10}\right ) \, dx=\frac {1}{30} \left (6+e^{10}\right ) x \]

[In]

Int[(6 + E^10)/30,x]

[Out]

((6 + E^10)*x)/30

Rule 8

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

Rubi steps \begin{align*} \text {integral}& = \frac {1}{30} \left (6+e^{10}\right ) x \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.93 \[ \int \frac {1}{30} \left (6+e^{10}\right ) \, dx=\frac {x}{5}+\frac {e^{10} x}{30} \]

[In]

Integrate[(6 + E^10)/30,x]

[Out]

x/5 + (E^10*x)/30

Maple [A] (verified)

Time = 0.01 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.53

method	result	size
default	\(\frac {x \left ({\mathrm e}^{10}+6\right )}{30}\)	\(8\)
norman	\(\left (\frac {{\mathrm e}^{10}}{30}+\frac {1}{5}\right ) x\)	\(9\)
parallelrisch	\(\left (\frac {{\mathrm e}^{10}}{30}+\frac {1}{5}\right ) x\)	\(9\)
risch	\(\frac {x \,{\mathrm e}^{10}}{30}+\frac {x}{5}\)	\(10\)
parts	\(\frac {x \,{\mathrm e}^{10}}{30}+\frac {x}{5}\)	\(10\)

[In]

int(1/30*exp(10)+1/5,x,method=_RETURNVERBOSE)

[Out]

1/30*x*(exp(10)+6)

Fricas [A] (verification not implemented)

none

Time = 0.23 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.60 \[ \int \frac {1}{30} \left (6+e^{10}\right ) \, dx=\frac {1}{30} \, x e^{10} + \frac {1}{5} \, x \]

[In]

integrate(1/30*exp(10)+1/5,x, algorithm="fricas")

[Out]

1/30*x*e^10 + 1/5*x

Sympy [A] (verification not implemented)

Time = 0.01 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.53 \[ \int \frac {1}{30} \left (6+e^{10}\right ) \, dx=x \left (\frac {1}{5} + \frac {e^{10}}{30}\right ) \]

[In]

integrate(1/30*exp(10)+1/5,x)

[Out]

x*(1/5 + exp(10)/30)

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.47 \[ \int \frac {1}{30} \left (6+e^{10}\right ) \, dx=\frac {1}{30} \, x {\left (e^{10} + 6\right )} \]

[In]

integrate(1/30*exp(10)+1/5,x, algorithm="maxima")

[Out]

1/30*x*(e^10 + 6)

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.47 \[ \int \frac {1}{30} \left (6+e^{10}\right ) \, dx=\frac {1}{30} \, x {\left (e^{10} + 6\right )} \]

[In]

integrate(1/30*exp(10)+1/5,x, algorithm="giac")

[Out]

1/30*x*(e^10 + 6)

Mupad [B] (verification not implemented)

Time = 0.00 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.53 \[ \int \frac {1}{30} \left (6+e^{10}\right ) \, dx=x\,\left (\frac {{\mathrm {e}}^{10}}{30}+\frac {1}{5}\right ) \]

[In]

int(exp(10)/30 + 1/5,x)

[Out]

x*(exp(10)/30 + 1/5)