3.50.23 \(\int \frac {1-3 e^{23-3 x}}{\log (16)} \, dx\)

Optimal. Leaf size=23 \[ \frac {1-e^4+e^{-1-4 (-6+x)+x}+x}{\log (16)} \]

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Rubi [A]  time = 0.01, antiderivative size = 19, normalized size of antiderivative = 0.83, 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*} \frac {x}{\log (16)}+\frac {e^{23-3 x}}{\log (16)} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(1 - 3*E^(23 - 3*x))/Log[16],x]

[Out]

E^(23 - 3*x)/Log[16] + x/Log[16]

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 {\int \left (1-3 e^{23-3 x}\right ) \, dx}{\log (16)}\\ &=\frac {x}{\log (16)}-\frac {3 \int e^{23-3 x} \, dx}{\log (16)}\\ &=\frac {e^{23-3 x}}{\log (16)}+\frac {x}{\log (16)}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.01, size = 14, normalized size = 0.61 \begin {gather*} \frac {e^{23-3 x}+x}{\log (16)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(1 - 3*E^(23 - 3*x))/Log[16],x]

[Out]

(E^(23 - 3*x) + x)/Log[16]

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fricas [A]  time = 1.14, size = 14, normalized size = 0.61 \begin {gather*} \frac {x + e^{\left (-3 \, x + 23\right )}}{4 \, \log \relax (2)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/4*(-3*exp(-3*x+23)+1)/log(2),x, algorithm="fricas")

[Out]

1/4*(x + e^(-3*x + 23))/log(2)

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giac [A]  time = 0.12, size = 14, normalized size = 0.61 \begin {gather*} \frac {x + e^{\left (-3 \, x + 23\right )}}{4 \, \log \relax (2)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/4*(-3*exp(-3*x+23)+1)/log(2),x, algorithm="giac")

[Out]

1/4*(x + e^(-3*x + 23))/log(2)

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maple [A]  time = 0.04, size = 15, normalized size = 0.65

method	result	size
default	\(\frac {x +{\mathrm e}^{-3 x +23}}{4 \ln \relax (2)}\)	\(15\)
norman	\(\frac {x}{4 \ln \relax (2)}+\frac {{\mathrm e}^{-3 x +23}}{4 \ln \relax (2)}\)	\(21\)
risch	\(\frac {x}{4 \ln \relax (2)}+\frac {{\mathrm e}^{-3 x +23}}{4 \ln \relax (2)}\)	\(21\)
derivativedivides	\(-\frac {-3 \,{\mathrm e}^{-3 x +23}+\ln \left ({\mathrm e}^{-3 x +23}\right )}{12 \ln \relax (2)}\)	\(23\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/4*(-3*exp(-3*x+23)+1)/ln(2),x,method=_RETURNVERBOSE)

[Out]

1/4/ln(2)*(x+exp(-3*x+23))

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maxima [A]  time = 0.34, size = 14, normalized size = 0.61 \begin {gather*} \frac {x + e^{\left (-3 \, x + 23\right )}}{4 \, \log \relax (2)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/4*(-3*exp(-3*x+23)+1)/log(2),x, algorithm="maxima")

[Out]

1/4*(x + e^(-3*x + 23))/log(2)

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mupad [B]  time = 0.07, size = 18, normalized size = 0.78 \begin {gather*} \frac {3\,x+3\,{\mathrm {e}}^{23-3\,x}}{12\,\ln \relax (2)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-((3*exp(23 - 3*x))/4 - 1/4)/log(2),x)

[Out]

(3*x + 3*exp(23 - 3*x))/(12*log(2))

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sympy [A]  time = 0.10, size = 17, normalized size = 0.74 \begin {gather*} \frac {x}{4 \log {\relax (2 )}} + \frac {e^{23 - 3 x}}{4 \log {\relax (2 )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/4*(-3*exp(-3*x+23)+1)/ln(2),x)

[Out]

x/(4*log(2)) + exp(23 - 3*x)/(4*log(2))

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