3.102.68 \(\int (-25-2 e^2) \, dx\)

Optimal. Leaf size=14 \[ 25 (2-x)-2 e^2 x \]

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Rubi [A]  time = 0.00, antiderivative size = 10, normalized size of antiderivative = 0.71, number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {8} \begin {gather*} -\left (\left (25+2 e^2\right ) x\right ) \end {gather*}

Antiderivative was successfully verified.

[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 {gather*} \begin {aligned} \text {integral} &=-\left (\left (25+2 e^2\right ) x\right )\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 10, normalized size = 0.71 \begin {gather*} -25 x-2 e^2 x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-25 - 2*E^2,x]

[Out]

-25*x - 2*E^2*x

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fricas [A]  time = 0.81, size = 9, normalized size = 0.64 \begin {gather*} -2 \, x e^{2} - 25 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-2*x*e^2 - 25*x

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giac [A]  time = 0.23, size = 9, normalized size = 0.64 \begin {gather*} -x {\left (2 \, e^{2} + 25\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-x*(2*e^2 + 25)

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maple [A]  time = 0.01, size = 10, normalized size = 0.71

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.34, size = 9, normalized size = 0.64 \begin {gather*} -x {\left (2 \, e^{2} + 25\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-x*(2*e^2 + 25)

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mupad [B]  time = 0.00, size = 9, normalized size = 0.64 \begin {gather*} -x\,\left (2\,{\mathrm {e}}^2+25\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(- 2*exp(2) - 25,x)

[Out]

-x*(2*exp(2) + 25)

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sympy [A]  time = 0.05, size = 8, normalized size = 0.57 \begin {gather*} x \left (-25 - 2 e^{2}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x*(-25 - 2*exp(2))

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