\(\int \frac {e^{11+x} (1+2 \log (3))}{\log (3)} \, dx\) [10120]

Optimal result

Integrand size = 16, antiderivative size = 12 \[ \int \frac {e^{11+x} (1+2 \log (3))}{\log (3)} \, dx=e^{11+x} \left (2+\frac {1}{\log (3)}\right ) \]

[Out]

exp(11+ln(1/ln(3)+2)+x)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {12, 2225} \[ \int \frac {e^{11+x} (1+2 \log (3))}{\log (3)} \, dx=\frac {e^{x+11} (1+\log (9))}{\log (3)} \]

[In]

Int[(E^(11 + x)*(1 + 2*Log[3]))/Log[3],x]

[Out]

(E^(11 + x)*(1 + Log[9]))/Log[3]

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+\log (9)) \int e^{11+x} \, dx}{\log (3)} \\ & = \frac {e^{11+x} (1+\log (9))}{\log (3)} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.02 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {e^{11+x} (1+2 \log (3))}{\log (3)} \, dx=\frac {e^{11+x} (1+\log (9))}{\log (3)} \]

[In]

Integrate[(E^(11 + x)*(1 + 2*Log[3]))/Log[3],x]

[Out]

(E^(11 + x)*(1 + Log[9]))/Log[3]

Maple [A] (verified)

Time = 0.25 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.42

method	result	size
gosper	\({\mathrm e}^{\ln \left (\frac {2 \ln \left (3\right )+1}{\ln \left (3\right )}\right )+11+x}\)	\(17\)
derivativedivides	\({\mathrm e}^{\ln \left (\frac {2 \ln \left (3\right )+1}{\ln \left (3\right )}\right )+11+x}\)	\(17\)
default	\({\mathrm e}^{\ln \left (\frac {2 \ln \left (3\right )+1}{\ln \left (3\right )}\right )+11+x}\)	\(17\)
norman	\({\mathrm e}^{\ln \left (\frac {2 \ln \left (3\right )+1}{\ln \left (3\right )}\right )+11+x}\)	\(17\)
risch	\(2 \,{\mathrm e}^{11+x}+\frac {{\mathrm e}^{11+x}}{\ln \left (3\right )}\)	\(17\)
parallelrisch	\({\mathrm e}^{\ln \left (\frac {2 \ln \left (3\right )+1}{\ln \left (3\right )}\right )+11+x}\)	\(17\)
meijerg	\(-{\mathrm e}^{\ln \left (\frac {2 \ln \left (3\right )+1}{\ln \left (3\right )}\right )+11} \left (1-{\mathrm e}^{x}\right )\)	\(24\)

[In]

int(exp(ln((2*ln(3)+1)/ln(3))+11+x),x,method=_RETURNVERBOSE)

[Out]

exp(ln((2*ln(3)+1)/ln(3))+11+x)

Fricas [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.33 \[ \int \frac {e^{11+x} (1+2 \log (3))}{\log (3)} \, dx=e^{\left (x + \log \left (\frac {2 \, \log \left (3\right ) + 1}{\log \left (3\right )}\right ) + 11\right )} \]

[In]

integrate(exp(log((2*log(3)+1)/log(3))+11+x),x, algorithm="fricas")

[Out]

e^(x + log((2*log(3) + 1)/log(3)) + 11)

Sympy [A] (verification not implemented)

Time = 0.07 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {e^{11+x} (1+2 \log (3))}{\log (3)} \, dx=\frac {\left (1 + 2 \log {\left (3 \right )}\right ) e^{x + 11}}{\log {\left (3 \right )}} \]

[In]

integrate(exp(ln((2*ln(3)+1)/ln(3))+11+x),x)

[Out]

(1 + 2*log(3))*exp(x + 11)/log(3)

Maxima [A] (verification not implemented)

none

Time = 0.18 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.25 \[ \int \frac {e^{11+x} (1+2 \log (3))}{\log (3)} \, dx=\frac {{\left (2 \, \log \left (3\right ) + 1\right )} e^{\left (x + 11\right )}}{\log \left (3\right )} \]

[In]

integrate(exp(log((2*log(3)+1)/log(3))+11+x),x, algorithm="maxima")

[Out]

(2*log(3) + 1)*e^(x + 11)/log(3)

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.33 \[ \int \frac {e^{11+x} (1+2 \log (3))}{\log (3)} \, dx=e^{\left (x + \log \left (\frac {2 \, \log \left (3\right ) + 1}{\log \left (3\right )}\right ) + 11\right )} \]

[In]

integrate(exp(log((2*log(3)+1)/log(3))+11+x),x, algorithm="giac")

[Out]

e^(x + log((2*log(3) + 1)/log(3)) + 11)

Mupad [B] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.25 \[ \int \frac {e^{11+x} (1+2 \log (3))}{\log (3)} \, dx=\frac {{\mathrm {e}}^{11}\,{\mathrm {e}}^x\,\left (2\,\ln \left (3\right )+1\right )}{\ln \left (3\right )} \]

[In]

int(exp(x + log((2*log(3) + 1)/log(3)) + 11),x)

[Out]

(exp(11)*exp(x)*(2*log(3) + 1))/log(3)