3.101.63 \(\int \frac {1}{24} (25+24 e^x) \, dx\)

Optimal. Leaf size=9 \[ e^x+\frac {25 x}{24} \]

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Rubi [A]  time = 0.00, antiderivative size = 9, normalized size of antiderivative = 1.00, 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 {25 x}{24}+e^x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(25 + 24*E^x)/24,x]

[Out]

E^x + (25*x)/24

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}{24} \int \left (25+24 e^x\right ) \, dx\\ &=\frac {25 x}{24}+\int e^x \, dx\\ &=e^x+\frac {25 x}{24}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 9, normalized size = 1.00 \begin {gather*} e^x+\frac {25 x}{24} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(25 + 24*E^x)/24,x]

[Out]

E^x + (25*x)/24

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fricas [A]  time = 0.69, size = 6, normalized size = 0.67 \begin {gather*} \frac {25}{24} \, x + e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x)+25/24,x, algorithm="fricas")

[Out]

25/24*x + e^x

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giac [A]  time = 0.13, size = 6, normalized size = 0.67 \begin {gather*} \frac {25}{24} \, x + e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x)+25/24,x, algorithm="giac")

[Out]

25/24*x + e^x

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maple [A]  time = 0.02, size = 7, normalized size = 0.78

method	result	size
default	\(\frac {25 x}{24}+{\mathrm e}^{x}\)	\(7\)
norman	\(\frac {25 x}{24}+{\mathrm e}^{x}\)	\(7\)
risch	\(\frac {25 x}{24}+{\mathrm e}^{x}\)	\(7\)
derivativedivides	\({\mathrm e}^{x}+\frac {25 \ln \left ({\mathrm e}^{x}\right )}{24}\)	\(9\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(x)+25/24,x,method=_RETURNVERBOSE)

[Out]

25/24*x+exp(x)

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maxima [A]  time = 0.36, size = 6, normalized size = 0.67 \begin {gather*} \frac {25}{24} \, x + e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x)+25/24,x, algorithm="maxima")

[Out]

25/24*x + e^x

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mupad [B]  time = 6.86, size = 6, normalized size = 0.67 \begin {gather*} \frac {25\,x}{24}+{\mathrm {e}}^x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(x) + 25/24,x)

[Out]

(25*x)/24 + exp(x)

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sympy [A]  time = 0.07, size = 7, normalized size = 0.78 \begin {gather*} \frac {25 x}{24} + e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x)+25/24,x)

[Out]

25*x/24 + exp(x)

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