\(\int \frac {2-e^4}{x} \, dx\) [8397]

Optimal result

Integrand size = 11, antiderivative size = 16 \[ \int \frac {2-e^4}{x} \, dx=-\frac {1}{8}+\left (2-e^4\right ) \log (5 x) \]

[Out]

(2-exp(4))*ln(5*x)-1/8

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.62, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {12, 29} \[ \int \frac {2-e^4}{x} \, dx=\left (2-e^4\right ) \log (x) \]

[In]

Int[(2 - E^4)/x,x]

[Out]

(2 - E^4)*Log[x]

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 29

Int[(x_)^(-1), x_Symbol] :> Simp[Log[x], x]

Rubi steps \begin{align*} \text {integral}& = \left (2-e^4\right ) \int \frac {1}{x} \, dx \\ & = \left (2-e^4\right ) \log (x) \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.62 \[ \int \frac {2-e^4}{x} \, dx=\left (2-e^4\right ) \log (x) \]

[In]

Integrate[(2 - E^4)/x,x]

[Out]

(2 - E^4)*Log[x]

Maple [A] (verified)

Time = 0.06 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.62

method	result	size
default	\(\left (2-{\mathrm e}^{4}\right ) \ln \left (x \right )\)	\(10\)
norman	\(\left (2-{\mathrm e}^{4}\right ) \ln \left (x \right )\)	\(10\)
parallelrisch	\(\left (2-{\mathrm e}^{4}\right ) \ln \left (x \right )\)	\(10\)
risch	\(-{\mathrm e}^{4} \ln \left (x \right )+2 \ln \left (x \right )\)	\(12\)

[In]

int((2-exp(4))/x,x,method=_RETURNVERBOSE)

[Out]

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

Fricas [A] (verification not implemented)

none

Time = 0.23 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.50 \[ \int \frac {2-e^4}{x} \, dx=-{\left (e^{4} - 2\right )} \log \left (x\right ) \]

[In]

integrate((2-exp(4))/x,x, algorithm="fricas")

[Out]

-(e^4 - 2)*log(x)

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.44 \[ \int \frac {2-e^4}{x} \, dx=\left (2 - e^{4}\right ) \log {\left (x \right )} \]

[In]

integrate((2-exp(4))/x,x)

[Out]

(2 - exp(4))*log(x)

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.50 \[ \int \frac {2-e^4}{x} \, dx=-{\left (e^{4} - 2\right )} \log \left (x\right ) \]

[In]

integrate((2-exp(4))/x,x, algorithm="maxima")

[Out]

-(e^4 - 2)*log(x)

Giac [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.56 \[ \int \frac {2-e^4}{x} \, dx=-{\left (e^{4} - 2\right )} \log \left ({\left | x \right |}\right ) \]

[In]

integrate((2-exp(4))/x,x, algorithm="giac")

[Out]

-(e^4 - 2)*log(abs(x))

Mupad [B] (verification not implemented)

Time = 14.04 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.50 \[ \int \frac {2-e^4}{x} \, dx=-\ln \left (x\right )\,\left ({\mathrm {e}}^4-2\right ) \]

[In]

int(-(exp(4) - 2)/x,x)

[Out]

-log(x)*(exp(4) - 2)