\(\int (-25-2 e^2) \, dx\) [10168]

Optimal result

Integrand size = 7, antiderivative size = 14 \[ \int \left (-25-2 e^2\right ) \, dx=25 (2-x)-2 e^2 x \]

[Out]

-25*x+50-2*x*exp(1)^2

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.71, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {8} \[ \int \left (-25-2 e^2\right ) \, dx=-\left (\left (25+2 e^2\right ) x\right ) \]

[In]

Int[-25 - 2*E^2,x]

[Out]

-((25 + 2*E^2)*x)

Rule 8

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

Rubi steps \begin{align*} \text {integral}& = -\left (\left (25+2 e^2\right ) x\right ) \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.71 \[ \int \left (-25-2 e^2\right ) \, dx=-25 x-2 e^2 x \]

[In]

Integrate[-25 - 2*E^2,x]

[Out]

-25*x - 2*E^2*x

Maple [A] (verified)

Time = 0.02 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.71

method	result	size
risch	\(-2 \,{\mathrm e}^{2} x -25 x\)	\(10\)
default	\(x \left (-2 \,{\mathrm e}^{2}-25\right )\)	\(11\)
norman	\(x \left (-2 \,{\mathrm e}^{2}-25\right )\)	\(11\)
parallelrisch	\(x \left (-2 \,{\mathrm e}^{2}-25\right )\)	\(11\)
parts	\(-2 \,{\mathrm e}^{2} x -25 x\)	\(12\)

[In]

int(-2*exp(1)^2-25,x,method=_RETURNVERBOSE)

[Out]

-2*exp(2)*x-25*x

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.64 \[ \int \left (-25-2 e^2\right ) \, dx=-2 \, x e^{2} - 25 \, x \]

[In]

integrate(-2*exp(1)^2-25,x, algorithm="fricas")

[Out]

-2*x*e^2 - 25*x

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.57 \[ \int \left (-25-2 e^2\right ) \, dx=x \left (-25 - 2 e^{2}\right ) \]

[In]

integrate(-2*exp(1)**2-25,x)

[Out]

x*(-25 - 2*exp(2))

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.64 \[ \int \left (-25-2 e^2\right ) \, dx=-x {\left (2 \, e^{2} + 25\right )} \]

[In]

integrate(-2*exp(1)^2-25,x, algorithm="maxima")

[Out]

-x*(2*e^2 + 25)

Giac [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.64 \[ \int \left (-25-2 e^2\right ) \, dx=-x {\left (2 \, e^{2} + 25\right )} \]

[In]

integrate(-2*exp(1)^2-25,x, algorithm="giac")

[Out]

-x*(2*e^2 + 25)

Mupad [B] (verification not implemented)

Time = 0.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.64 \[ \int \left (-25-2 e^2\right ) \, dx=-x\,\left (2\,{\mathrm {e}}^2+25\right ) \]

[In]

int(- 2*exp(2) - 25,x)

[Out]

-x*(2*exp(2) + 25)