3.54.61 \(\int (-e^x+\log (5)) \, dx\)

Optimal. Leaf size=13 \[ -3-e^x+\log (2)+x \log (5) \]

________________________________________________________________________________________

Rubi [A]  time = 0.00, antiderivative size = 10, normalized size of antiderivative = 0.77, number of steps used = 2, number of rules used = 1, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {2194} \begin {gather*} x \log (5)-e^x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-E^x + Log[5],x]

[Out]

-E^x + x*Log[5]

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 (5)-\int e^x \, dx\\ &=-e^x+x \log (5)\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.00, size = 10, normalized size = 0.77 \begin {gather*} -e^x+x \log (5) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-E^x + Log[5],x]

[Out]

-E^x + x*Log[5]

________________________________________________________________________________________

fricas [A]  time = 0.57, size = 9, normalized size = 0.69 \begin {gather*} x \log \relax (5) - e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(x)+log(5),x, algorithm="fricas")

[Out]

x*log(5) - e^x

________________________________________________________________________________________

giac [A]  time = 0.13, size = 9, normalized size = 0.69 \begin {gather*} x \log \relax (5) - e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(x)+log(5),x, algorithm="giac")

[Out]

x*log(5) - e^x

________________________________________________________________________________________

maple [A]  time = 0.03, size = 10, normalized size = 0.77

method	result	size
default	\(-{\mathrm e}^{x}+x \ln \relax (5)\)	\(10\)
norman	\(-{\mathrm e}^{x}+x \ln \relax (5)\)	\(10\)
risch	\(-{\mathrm e}^{x}+x \ln \relax (5)\)	\(10\)
derivativedivides	\(-{\mathrm e}^{x}+\ln \relax (5) \ln \left ({\mathrm e}^{x}\right )\)	\(12\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-exp(x)+ln(5),x,method=_RETURNVERBOSE)

[Out]

-exp(x)+x*ln(5)

________________________________________________________________________________________

maxima [A]  time = 0.36, size = 9, normalized size = 0.69 \begin {gather*} x \log \relax (5) - e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(x)+log(5),x, algorithm="maxima")

[Out]

x*log(5) - e^x

________________________________________________________________________________________

mupad [B]  time = 0.04, size = 9, normalized size = 0.69 \begin {gather*} x\,\ln \relax (5)-{\mathrm {e}}^x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(log(5) - exp(x),x)

[Out]

x*log(5) - exp(x)

________________________________________________________________________________________

sympy [A]  time = 0.07, size = 7, normalized size = 0.54 \begin {gather*} x \log {\relax (5 )} - e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(x)+ln(5),x)

[Out]

x*log(5) - exp(x)

________________________________________________________________________________________