3.50.88 \(\int \frac {1}{2} (7+2 e^x) \, dx\)

Optimal. Leaf size=12 \[ -\frac {9}{4}+e^x+\frac {7 x}{2} \]

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Rubi [A]  time = 0.00, antiderivative size = 9, normalized size of antiderivative = 0.75, number of steps used = 3, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {12, 2194} \begin {gather*} \frac {7 x}{2}+e^x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(7 + 2*E^x)/2,x]

[Out]

E^x + (7*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 {1}{2} \int \left (7+2 e^x\right ) \, dx\\ &=\frac {7 x}{2}+\int e^x \, dx\\ &=e^x+\frac {7 x}{2}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 9, normalized size = 0.75 \begin {gather*} e^x+\frac {7 x}{2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(7 + 2*E^x)/2,x]

[Out]

E^x + (7*x)/2

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fricas [A]  time = 0.66, size = 6, normalized size = 0.50 \begin {gather*} \frac {7}{2} \, x + e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x)+7/2,x, algorithm="fricas")

[Out]

7/2*x + e^x

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giac [A]  time = 0.13, size = 6, normalized size = 0.50 \begin {gather*} \frac {7}{2} \, x + e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x)+7/2,x, algorithm="giac")

[Out]

7/2*x + e^x

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maple [A]  time = 0.02, size = 7, normalized size = 0.58

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(x)+7/2,x,method=_RETURNVERBOSE)

[Out]

7/2*x+exp(x)

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maxima [A]  time = 0.35, size = 6, normalized size = 0.50 \begin {gather*} \frac {7}{2} \, x + e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x)+7/2,x, algorithm="maxima")

[Out]

7/2*x + e^x

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mupad [B]  time = 0.03, size = 6, normalized size = 0.50 \begin {gather*} \frac {7\,x}{2}+{\mathrm {e}}^x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(x) + 7/2,x)

[Out]

(7*x)/2 + exp(x)

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sympy [A]  time = 0.06, size = 7, normalized size = 0.58 \begin {gather*} \frac {7 x}{2} + e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x)+7/2,x)

[Out]

7*x/2 + exp(x)

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