3.29.18 \(\int (-\log (2)+3 e^{2+x} \log (2)) \, dx\)

Optimal. Leaf size=25 \[ 3 \left (6+\left (-e+e^{2+x}+\frac {2-x}{3}\right ) \log (2)\right ) \]

________________________________________________________________________________________

Rubi [A]  time = 0.01, antiderivative size = 15, normalized size of antiderivative = 0.60, number of steps used = 2, number of rules used = 1, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {2194} \begin {gather*} 3 e^{x+2} \log (2)-x \log (2) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-Log[2] + 3*E^(2 + x)*Log[2],x]

[Out]

3*E^(2 + x)*Log[2] - x*Log[2]

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} &=-x \log (2)+(3 \log (2)) \int e^{2+x} \, dx\\ &=3 e^{2+x} \log (2)-x \log (2)\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.00, size = 14, normalized size = 0.56 \begin {gather*} \left (3 e^{2+x}-x\right ) \log (2) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-Log[2] + 3*E^(2 + x)*Log[2],x]

[Out]

(3*E^(2 + x) - x)*Log[2]

________________________________________________________________________________________

fricas [A]  time = 0.75, size = 14, normalized size = 0.56 \begin {gather*} -x \log \relax (2) + 3 \, e^{\left (x + 2\right )} \log \relax (2) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3*log(2)*exp(2+x)-log(2),x, algorithm="fricas")

[Out]

-x*log(2) + 3*e^(x + 2)*log(2)

________________________________________________________________________________________

giac [A]  time = 0.22, size = 14, normalized size = 0.56 \begin {gather*} -x \log \relax (2) + 3 \, e^{\left (x + 2\right )} \log \relax (2) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3*log(2)*exp(2+x)-log(2),x, algorithm="giac")

[Out]

-x*log(2) + 3*e^(x + 2)*log(2)

________________________________________________________________________________________

maple [A]  time = 0.02, size = 15, normalized size = 0.60

method	result	size
default	\(3 \ln \relax (2) {\mathrm e}^{2+x}-x \ln \relax (2)\)	\(15\)
norman	\(3 \ln \relax (2) {\mathrm e}^{2+x}-x \ln \relax (2)\)	\(15\)
risch	\(3 \ln \relax (2) {\mathrm e}^{2+x}-x \ln \relax (2)\)	\(15\)
derivativedivides	\(\ln \relax (2) \left (3 \,{\mathrm e}^{2+x}-\ln \left ({\mathrm e}^{2+x}\right )\right )\)	\(18\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(3*ln(2)*exp(2+x)-ln(2),x,method=_RETURNVERBOSE)

[Out]

3*ln(2)*exp(2+x)-x*ln(2)

________________________________________________________________________________________

maxima [A]  time = 0.40, size = 14, normalized size = 0.56 \begin {gather*} -x \log \relax (2) + 3 \, e^{\left (x + 2\right )} \log \relax (2) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3*log(2)*exp(2+x)-log(2),x, algorithm="maxima")

[Out]

-x*log(2) + 3*e^(x + 2)*log(2)

________________________________________________________________________________________

mupad [B]  time = 0.07, size = 12, normalized size = 0.48 \begin {gather*} -\ln \relax (2)\,\left (x-3\,{\mathrm {e}}^2\,{\mathrm {e}}^x\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(3*exp(x + 2)*log(2) - log(2),x)

[Out]

-log(2)*(x - 3*exp(2)*exp(x))

________________________________________________________________________________________

sympy [A]  time = 0.08, size = 14, normalized size = 0.56 \begin {gather*} - x \log {\relax (2 )} + 3 e^{x + 2} \log {\relax (2 )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3*ln(2)*exp(2+x)-ln(2),x)

[Out]

-x*log(2) + 3*exp(x + 2)*log(2)

________________________________________________________________________________________