3.43.89 \(\int \frac {1}{9} (18+44 e^{10}) \, dx\)

Optimal. Leaf size=13 \[ -7+2 x+\frac {44 e^{10} x}{9} \]

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Rubi [A]  time = 0.00, antiderivative size = 12, normalized size of antiderivative = 0.92, number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {8} \begin {gather*} \frac {2}{9} \left (9+22 e^{10}\right ) x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(18 + 44*E^10)/9,x]

[Out]

(2*(9 + 22*E^10)*x)/9

Rule 8

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

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {2}{9} \left (9+22 e^{10}\right ) x\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 12, normalized size = 0.92 \begin {gather*} 2 x+\frac {44 e^{10} x}{9} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(18 + 44*E^10)/9,x]

[Out]

2*x + (44*E^10*x)/9

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fricas [A]  time = 0.44, size = 9, normalized size = 0.69 \begin {gather*} \frac {44}{9} \, x e^{10} + 2 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(44/9*exp(5)^2+2,x, algorithm="fricas")

[Out]

44/9*x*e^10 + 2*x

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giac [A]  time = 0.13, size = 9, normalized size = 0.69 \begin {gather*} \frac {2}{9} \, x {\left (22 \, e^{10} + 9\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(44/9*exp(5)^2+2,x, algorithm="giac")

[Out]

2/9*x*(22*e^10 + 9)

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maple [A]  time = 0.01, size = 10, normalized size = 0.77

method	result	size
risch	\(\frac {44 x \,{\mathrm e}^{10}}{9}+2 x\)	\(10\)
default	\(\left (\frac {44 \,{\mathrm e}^{10}}{9}+2\right ) x\)	\(11\)
norman	\(\left (\frac {44 \,{\mathrm e}^{10}}{9}+2\right ) x\)	\(11\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(44/9*exp(5)^2+2,x,method=_RETURNVERBOSE)

[Out]

44/9*x*exp(10)+2*x

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maxima [A]  time = 0.35, size = 9, normalized size = 0.69 \begin {gather*} \frac {2}{9} \, x {\left (22 \, e^{10} + 9\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(44/9*exp(5)^2+2,x, algorithm="maxima")

[Out]

2/9*x*(22*e^10 + 9)

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mupad [B]  time = 0.00, size = 8, normalized size = 0.62 \begin {gather*} x\,\left (\frac {44\,{\mathrm {e}}^{10}}{9}+2\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((44*exp(10))/9 + 2,x)

[Out]

x*((44*exp(10))/9 + 2)

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sympy [A]  time = 0.04, size = 8, normalized size = 0.62 \begin {gather*} x \left (2 + \frac {44 e^{10}}{9}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(44/9*exp(5)**2+2,x)

[Out]

x*(2 + 44*exp(10)/9)

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