3.69.26 \(\int (5+e) \, dx\)

Optimal. Leaf size=18 \[ x \left (5+e-\frac {\log \left (5 e^{e^2}\right )}{x}\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 5, normalized size of antiderivative = 0.28, number of steps used = 1, number of rules used = 1, integrand size = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.333, Rules used = {8} \begin {gather*} (5+e) x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[5 + E,x]

[Out]

(5 + E)*x

Rule 8

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

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=(5+e) x\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 7, normalized size = 0.39 \begin {gather*} 5 x+e x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[5 + E,x]

[Out]

5*x + E*x

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fricas [A]  time = 0.50, size = 8, normalized size = 0.44 \begin {gather*} x e + 5 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x*e + 5*x

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giac [A]  time = 0.14, size = 6, normalized size = 0.33 \begin {gather*} x {\left (e + 5\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x*(e + 5)

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maple [A]  time = 0.01, size = 7, normalized size = 0.39

method	result	size
default	\(\left ({\mathrm e}+5\right ) x\)	\(7\)
norman	\(\left ({\mathrm e}+5\right ) x\)	\(7\)
risch	\(x \,{\mathrm e}+5 x\)	\(9\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

(exp(1)+5)*x

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maxima [A]  time = 0.36, size = 6, normalized size = 0.33 \begin {gather*} x {\left (e + 5\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x*(e + 5)

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mupad [B]  time = 0.00, size = 6, normalized size = 0.33 \begin {gather*} x\,\left (\mathrm {e}+5\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(1) + 5,x)

[Out]

x*(exp(1) + 5)

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sympy [A]  time = 0.05, size = 5, normalized size = 0.28 \begin {gather*} x \left (e + 5\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(1)+5,x)

[Out]

x*(E + 5)

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