\(\int \frac {1}{24} (25+24 e^x) \, dx\) [10063]

Optimal result

Integrand size = 11, antiderivative size = 9 \[ \int \frac {1}{24} \left (25+24 e^x\right ) \, dx=e^x+\frac {25 x}{24} \]

[Out]

25/24*x+exp(x)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {12, 2225} \[ \int \frac {1}{24} \left (25+24 e^x\right ) \, dx=\frac {25 x}{24}+e^x \]

[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 2225

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{align*} \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{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.00 \[ \int \frac {1}{24} \left (25+24 e^x\right ) \, dx=e^x+\frac {25 x}{24} \]

[In]

Integrate[(25 + 24*E^x)/24,x]

[Out]

E^x + (25*x)/24

Maple [A] (verified)

Time = 0.18 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.78

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

[In]

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

[Out]

25/24*x+exp(x)

Fricas [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.67 \[ \int \frac {1}{24} \left (25+24 e^x\right ) \, dx=\frac {25}{24} \, x + e^{x} \]

[In]

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

[Out]

25/24*x + e^x

Sympy [A] (verification not implemented)

Time = 0.04 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.78 \[ \int \frac {1}{24} \left (25+24 e^x\right ) \, dx=\frac {25 x}{24} + e^{x} \]

[In]

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

[Out]

25*x/24 + exp(x)

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.67 \[ \int \frac {1}{24} \left (25+24 e^x\right ) \, dx=\frac {25}{24} \, x + e^{x} \]

[In]

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

[Out]

25/24*x + e^x

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.67 \[ \int \frac {1}{24} \left (25+24 e^x\right ) \, dx=\frac {25}{24} \, x + e^{x} \]

[In]

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

[Out]

25/24*x + e^x

Mupad [B] (verification not implemented)

Time = 15.62 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.67 \[ \int \frac {1}{24} \left (25+24 e^x\right ) \, dx=\frac {25\,x}{24}+{\mathrm {e}}^x \]

[In]

int(exp(x) + 25/24,x)

[Out]

(25*x)/24 + exp(x)