3.96.53 \(\int \frac {1}{2} (2 e+x) \, dx\)

Optimal. Leaf size=11 \[ \left (-e-\frac {x}{2}\right )^2 \]

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Rubi [A]  time = 0.00, antiderivative size = 11, normalized size of antiderivative = 1.00, 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 = {9} \begin {gather*} \frac {1}{4} (x+2 e)^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(2*E + x)/2,x]

[Out]

(2*E + x)^2/4

Rule 9

Int[(a_)*((b_) + (c_.)*(x_)), x_Symbol] :> Simp[(a*(b + c*x)^2)/(2*c), x] /; FreeQ[{a, b, c}, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{4} (2 e+x)^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 11, normalized size = 1.00 \begin {gather*} e x+\frac {x^2}{4} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(2*E + x)/2,x]

[Out]

E*x + x^2/4

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fricas [A]  time = 0.51, size = 10, normalized size = 0.91 \begin {gather*} \frac {1}{4} \, x^{2} + x e \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/4*x^2 + x*e

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giac [A]  time = 0.13, size = 10, normalized size = 0.91 \begin {gather*} \frac {1}{4} \, x^{2} + x e \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/4*x^2 + x*e

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maple [A]  time = 0.02, size = 10, normalized size = 0.91

method	result	size
gosper	\(\frac {x \left (x +4 \,{\mathrm e}\right )}{4}\)	\(10\)
default	\(x \,{\mathrm e}+\frac {x^{2}}{4}\)	\(11\)
norman	\(x \,{\mathrm e}+\frac {x^{2}}{4}\)	\(11\)
risch	\(x \,{\mathrm e}+\frac {x^{2}}{4}\)	\(11\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/4*x*(x+4*exp(1))

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maxima [A]  time = 0.35, size = 10, normalized size = 0.91 \begin {gather*} \frac {1}{4} \, x^{2} + x e \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/4*x^2 + x*e

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mupad [B]  time = 0.04, size = 9, normalized size = 0.82 \begin {gather*} \frac {x\,\left (x+4\,\mathrm {e}\right )}{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x/2 + exp(1),x)

[Out]

(x*(x + 4*exp(1)))/4

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sympy [A]  time = 0.05, size = 8, normalized size = 0.73 \begin {gather*} \frac {x^{2}}{4} + e x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x**2/4 + E*x

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