3.10.48 \(\int 4 e^{4+x} \log (2) \, dx\)

Optimal. Leaf size=19 \[ 4 \left (1-\left (\frac {43}{6}-e^{4+x}\right ) \log (2)\right ) \]

________________________________________________________________________________________

Rubi [A]  time = 0.00, antiderivative size = 9, normalized size of antiderivative = 0.47, number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {12, 2194} \begin {gather*} 4 e^{x+4} \log (2) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[4*E^(4 + x)*Log[2],x]

[Out]

4*E^(4 + x)*Log[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} &=(4 \log (2)) \int e^{4+x} \, dx\\ &=4 e^{4+x} \log (2)\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.00, size = 8, normalized size = 0.42 \begin {gather*} e^{4+x} \log (16) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[4*E^(4 + x)*Log[2],x]

[Out]

E^(4 + x)*Log[16]

________________________________________________________________________________________

fricas [A]  time = 0.67, size = 8, normalized size = 0.42 \begin {gather*} 4 \, e^{\left (x + 4\right )} \log \relax (2) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4*log(2)*exp(4+x),x, algorithm="fricas")

[Out]

4*e^(x + 4)*log(2)

________________________________________________________________________________________

giac [A]  time = 0.33, size = 8, normalized size = 0.42 \begin {gather*} 4 \, e^{\left (x + 4\right )} \log \relax (2) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4*log(2)*exp(4+x),x, algorithm="giac")

[Out]

4*e^(x + 4)*log(2)

________________________________________________________________________________________

maple [A]  time = 0.02, size = 9, normalized size = 0.47

method	result	size
gosper	\(4 \ln \relax (2) {\mathrm e}^{4+x}\)	\(9\)
derivativedivides	\(4 \ln \relax (2) {\mathrm e}^{4+x}\)	\(9\)
default	\(4 \ln \relax (2) {\mathrm e}^{4+x}\)	\(9\)
norman	\(4 \ln \relax (2) {\mathrm e}^{4+x}\)	\(9\)
risch	\(4 \ln \relax (2) {\mathrm e}^{4+x}\)	\(9\)
meijerg	\(-4 \ln \relax (2) {\mathrm e}^{4} \left (1-{\mathrm e}^{x}\right )\)	\(13\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(4*ln(2)*exp(4+x),x,method=_RETURNVERBOSE)

[Out]

4*ln(2)*exp(4+x)

________________________________________________________________________________________

maxima [A]  time = 0.63, size = 8, normalized size = 0.42 \begin {gather*} 4 \, e^{\left (x + 4\right )} \log \relax (2) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4*log(2)*exp(4+x),x, algorithm="maxima")

[Out]

4*e^(x + 4)*log(2)

________________________________________________________________________________________

mupad [B]  time = 0.04, size = 8, normalized size = 0.42 \begin {gather*} 4\,{\mathrm {e}}^4\,{\mathrm {e}}^x\,\ln \relax (2) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(4*exp(x + 4)*log(2),x)

[Out]

4*exp(4)*exp(x)*log(2)

________________________________________________________________________________________

sympy [A]  time = 0.08, size = 8, normalized size = 0.42 \begin {gather*} 4 e^{x + 4} \log {\relax (2 )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4*ln(2)*exp(4+x),x)

[Out]

4*exp(x + 4)*log(2)

________________________________________________________________________________________