3.70.37 \(\int \frac {1}{5} (255+5 e^5+4 e^x) \, dx\)

Optimal. Leaf size=17 \[ \left (51+e^5+\frac {4 e^x}{5 x}\right ) x \]

________________________________________________________________________________________

Rubi [A]  time = 0.02, antiderivative size = 15, normalized size of antiderivative = 0.88, number of steps used = 3, number of rules used = 2, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {12, 2194} \begin {gather*} \left (51+e^5\right ) x+\frac {4 e^x}{5} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(255 + 5*E^5 + 4*E^x)/5,x]

[Out]

(4*E^x)/5 + (51 + E^5)*x

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}{5} \int \left (255+5 e^5+4 e^x\right ) \, dx\\ &=\left (51+e^5\right ) x+\frac {4 \int e^x \, dx}{5}\\ &=\frac {4 e^x}{5}+\left (51+e^5\right ) x\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.00, size = 16, normalized size = 0.94 \begin {gather*} \frac {4 e^x}{5}+51 x+e^5 x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(255 + 5*E^5 + 4*E^x)/5,x]

[Out]

(4*E^x)/5 + 51*x + E^5*x

________________________________________________________________________________________

fricas [A]  time = 0.60, size = 12, normalized size = 0.71 \begin {gather*} x e^{5} + 51 \, x + \frac {4}{5} \, e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4/5*exp(x)+exp(5)+51,x, algorithm="fricas")

[Out]

x*e^5 + 51*x + 4/5*e^x

________________________________________________________________________________________

giac [A]  time = 0.22, size = 12, normalized size = 0.71 \begin {gather*} x e^{5} + 51 \, x + \frac {4}{5} \, e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4/5*exp(x)+exp(5)+51,x, algorithm="giac")

[Out]

x*e^5 + 51*x + 4/5*e^x

________________________________________________________________________________________

maple [A]  time = 0.03, size = 12, normalized size = 0.71

method	result	size
norman	\(\left ({\mathrm e}^{5}+51\right ) x +\frac {4 \,{\mathrm e}^{x}}{5}\)	\(12\)
default	\(51 x +\frac {4 \,{\mathrm e}^{x}}{5}+x \,{\mathrm e}^{5}\)	\(13\)
risch	\(51 x +\frac {4 \,{\mathrm e}^{x}}{5}+x \,{\mathrm e}^{5}\)	\(13\)
derivativedivides	\(\frac {4 \,{\mathrm e}^{x}}{5}+\frac {\left (5 \,{\mathrm e}^{5}+255\right ) \ln \left ({\mathrm e}^{x}\right )}{5}\)	\(17\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(4/5*exp(x)+exp(5)+51,x,method=_RETURNVERBOSE)

[Out]

(exp(5)+51)*x+4/5*exp(x)

________________________________________________________________________________________

maxima [A]  time = 0.37, size = 12, normalized size = 0.71 \begin {gather*} x e^{5} + 51 \, x + \frac {4}{5} \, e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4/5*exp(x)+exp(5)+51,x, algorithm="maxima")

[Out]

x*e^5 + 51*x + 4/5*e^x

________________________________________________________________________________________

mupad [B]  time = 0.05, size = 11, normalized size = 0.65 \begin {gather*} \frac {4\,{\mathrm {e}}^x}{5}+x\,\left ({\mathrm {e}}^5+51\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(5) + (4*exp(x))/5 + 51,x)

[Out]

(4*exp(x))/5 + x*(exp(5) + 51)

________________________________________________________________________________________

sympy [A]  time = 0.07, size = 12, normalized size = 0.71 \begin {gather*} x \left (51 + e^{5}\right ) + \frac {4 e^{x}}{5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4/5*exp(x)+exp(5)+51,x)

[Out]

x*(51 + exp(5)) + 4*exp(x)/5

________________________________________________________________________________________