3.77.41 \(\int \frac {1}{10} (4+5 e) \, dx\)

Optimal. Leaf size=27 \[ 1+\frac {1}{2} \left (-4 \left (-3 e^3-\frac {x}{5}\right )+e \left (e^4+x\right )\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 10, normalized size of antiderivative = 0.37, number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {8} \begin {gather*} \frac {1}{10} (4+5 e) x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(4 + 5*E)/10,x]

[Out]

((4 + 5*E)*x)/10

Rule 8

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

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{10} (4+5 e) x\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 12, normalized size = 0.44 \begin {gather*} \frac {2 x}{5}+\frac {e x}{2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(4 + 5*E)/10,x]

[Out]

(2*x)/5 + (E*x)/2

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fricas [A]  time = 2.07, size = 9, normalized size = 0.33 \begin {gather*} \frac {1}{2} \, x e + \frac {2}{5} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/2*exp(1)+2/5,x, algorithm="fricas")

[Out]

1/2*x*e + 2/5*x

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giac [A]  time = 0.16, size = 9, normalized size = 0.33 \begin {gather*} \frac {1}{10} \, x {\left (5 \, e + 4\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/2*exp(1)+2/5,x, algorithm="giac")

[Out]

1/10*x*(5*e + 4)

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maple [A]  time = 0.01, size = 9, normalized size = 0.33

method	result	size
default	\(\left (\frac {{\mathrm e}}{2}+\frac {2}{5}\right ) x\)	\(9\)
norman	\(\left (\frac {{\mathrm e}}{2}+\frac {2}{5}\right ) x\)	\(9\)
risch	\(\frac {x \,{\mathrm e}}{2}+\frac {2 x}{5}\)	\(10\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/2*exp(1)+2/5,x,method=_RETURNVERBOSE)

[Out]

(1/2*exp(1)+2/5)*x

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maxima [A]  time = 0.35, size = 9, normalized size = 0.33 \begin {gather*} \frac {1}{10} \, x {\left (5 \, e + 4\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/2*exp(1)+2/5,x, algorithm="maxima")

[Out]

1/10*x*(5*e + 4)

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mupad [B]  time = 0.00, size = 8, normalized size = 0.30 \begin {gather*} x\,\left (\frac {\mathrm {e}}{2}+\frac {2}{5}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(1)/2 + 2/5,x)

[Out]

x*(exp(1)/2 + 2/5)

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sympy [A]  time = 0.05, size = 8, normalized size = 0.30 \begin {gather*} x \left (\frac {2}{5} + \frac {e}{2}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/2*exp(1)+2/5,x)

[Out]

x*(2/5 + E/2)

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