\(\int (3+e^2) \, dx\) [903]

Optimal result

Integrand size = 5, antiderivative size = 18 \[ \int \left (3+e^2\right ) \, dx=3 (-5+x)+\log \left (\frac {3 e^{e^2 x}}{4}\right ) \]

[Out]

3*x-15+ln(3/4*exp(exp(2)*x))

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.39, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {8} \[ \int \left (3+e^2\right ) \, dx=\left (3+e^2\right ) x \]

[In]

Int[3 + E^2,x]

[Out]

(3 + E^2)*x

Rule 8

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

Rubi steps \begin{align*} \text {integral}& = \left (3+e^2\right ) x \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.50 \[ \int \left (3+e^2\right ) \, dx=3 x+e^2 x \]

[In]

Integrate[3 + E^2,x]

[Out]

3*x + E^2*x

Maple [A] (verified)

Time = 0.01 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.39

method	result	size
default	\(x \left ({\mathrm e}^{2}+3\right )\)	\(7\)
norman	\(x \left ({\mathrm e}^{2}+3\right )\)	\(7\)
parallelrisch	\(x \left ({\mathrm e}^{2}+3\right )\)	\(7\)
risch	\({\mathrm e}^{2} x +3 x\)	\(9\)
parts	\({\mathrm e}^{2} x +3 x\)	\(9\)

[In]

int(exp(2)+3,x,method=_RETURNVERBOSE)

[Out]

x*(exp(2)+3)

Fricas [A] (verification not implemented)

none

Time = 0.24 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.44 \[ \int \left (3+e^2\right ) \, dx=x e^{2} + 3 \, x \]

[In]

integrate(exp(2)+3,x, algorithm="fricas")

[Out]

x*e^2 + 3*x

Sympy [A] (verification not implemented)

Time = 0.01 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.28 \[ \int \left (3+e^2\right ) \, dx=x \left (3 + e^{2}\right ) \]

[In]

integrate(exp(2)+3,x)

[Out]

x*(3 + exp(2))

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.33 \[ \int \left (3+e^2\right ) \, dx=x {\left (e^{2} + 3\right )} \]

[In]

integrate(exp(2)+3,x, algorithm="maxima")

[Out]

x*(e^2 + 3)

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.33 \[ \int \left (3+e^2\right ) \, dx=x {\left (e^{2} + 3\right )} \]

[In]

integrate(exp(2)+3,x, algorithm="giac")

[Out]

x*(e^2 + 3)

Mupad [B] (verification not implemented)

Time = 0.00 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.33 \[ \int \left (3+e^2\right ) \, dx=x\,\left ({\mathrm {e}}^2+3\right ) \]

[In]

int(exp(2) + 3,x)

[Out]

x*(exp(2) + 3)