3.10.3 \(\int (3+e^2) \, dx\)

Optimal. Leaf size=18 \[ 3 (-5+x)+\log \left (\frac {3 e^{e^2 x}}{4}\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 7, normalized size of antiderivative = 0.39, number of steps used = 1, number of rules used = 1, integrand size = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {8} \begin {gather*} \left (3+e^2\right ) x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[3 + E^2,x]

[Out]

(3 + 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 (3+e^2\right ) x\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 9, normalized size = 0.50 \begin {gather*} 3 x+e^2 x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[3 + E^2,x]

[Out]

3*x + E^2*x

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fricas [A]  time = 0.50, size = 8, normalized size = 0.44 \begin {gather*} x e^{2} + 3 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(2)+3,x, algorithm="fricas")

[Out]

x*e^2 + 3*x

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giac [A]  time = 0.32, size = 6, normalized size = 0.33 \begin {gather*} x {\left (e^{2} + 3\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(2)+3,x, algorithm="giac")

[Out]

x*(e^2 + 3)

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

method	result	size
default	\(\left ({\mathrm e}^{2}+3\right ) x\)	\(7\)
norman	\(\left ({\mathrm e}^{2}+3\right ) x\)	\(7\)
risch	\({\mathrm e}^{2} x +3 x\)	\(9\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(2)+3,x,method=_RETURNVERBOSE)

[Out]

(exp(2)+3)*x

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maxima [A]  time = 0.49, size = 6, normalized size = 0.33 \begin {gather*} x {\left (e^{2} + 3\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(2)+3,x, algorithm="maxima")

[Out]

x*(e^2 + 3)

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mupad [B]  time = 0.00, size = 6, normalized size = 0.33 \begin {gather*} x\,\left ({\mathrm {e}}^2+3\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(2) + 3,x)

[Out]

x*(exp(2) + 3)

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sympy [A]  time = 0.04, size = 5, normalized size = 0.28 \begin {gather*} x \left (3 + e^{2}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(2)+3,x)

[Out]

x*(3 + exp(2))

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