3.37.44 \(\int \frac {5}{2} e^{\frac {2+x}{2}} \, dx\)

Optimal. Leaf size=13 \[ -5+5 e^{1+\frac {x}{2}} \]

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Rubi [A]  time = 0.00, antiderivative size = 11, normalized size of antiderivative = 0.85, number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {12, 2194} \begin {gather*} 5 e^{\frac {x+2}{2}} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(5*E^((2 + x)/2))/2,x]

[Out]

5*E^((2 + x)/2)

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 2194

Int[((F_)^((c_.)*((a_.) + (b_.)*(x_))))^(n_.), x_Symbol] :> Simp[(F^(c*(a + b*x)))^n/(b*c*n*Log[F]), x] /; Fre
eQ[{F, a, b, c, n}, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {5}{2} \int e^{\frac {2+x}{2}} \, dx\\ &=5 e^{\frac {2+x}{2}}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 11, normalized size = 0.85 \begin {gather*} 5 e^{1+\frac {x}{2}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(5*E^((2 + x)/2))/2,x]

[Out]

5*E^(1 + x/2)

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fricas [A]  time = 0.68, size = 8, normalized size = 0.62 \begin {gather*} 5 \, e^{\left (\frac {1}{2} \, x + 1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

5*e^(1/2*x + 1)

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giac [A]  time = 0.17, size = 8, normalized size = 0.62 \begin {gather*} 5 \, e^{\left (\frac {1}{2} \, x + 1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

5*e^(1/2*x + 1)

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maple [A]  time = 0.02, size = 9, normalized size = 0.69

method	result	size
gosper	\(5 \,{\mathrm e}^{1+\frac {x}{2}}\)	\(9\)
derivativedivides	\(5 \,{\mathrm e}^{1+\frac {x}{2}}\)	\(9\)
default	\(5 \,{\mathrm e}^{1+\frac {x}{2}}\)	\(9\)
norman	\(5 \,{\mathrm e}^{1+\frac {x}{2}}\)	\(9\)
risch	\(5 \,{\mathrm e}^{1+\frac {x}{2}}\)	\(9\)
meijerg	\(-5 \,{\mathrm e} \left (1-{\mathrm e}^{\frac {x}{2}}\right )\)	\(13\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.34, size = 8, normalized size = 0.62 \begin {gather*} 5 \, e^{\left (\frac {1}{2} \, x + 1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

5*e^(1/2*x + 1)

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mupad [B]  time = 2.14, size = 8, normalized size = 0.62 \begin {gather*} 5\,{\mathrm {e}}^{x/2}\,\mathrm {e} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((5*exp(x/2 + 1))/2,x)

[Out]

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

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sympy [A]  time = 0.07, size = 7, normalized size = 0.54 \begin {gather*} 5 e^{\frac {x}{2} + 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

5*exp(x/2 + 1)

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