\(\int \frac {1}{e^6 x} \, dx\) [9134]

Optimal result

Integrand size = 7, antiderivative size = 10 \[ \int \frac {1}{e^6 x} \, dx=8+\frac {4+\log (x)}{e^6} \]

[Out]

8+(ln(x)+4)/exp(6)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.60, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.286, Rules used = {12, 29} \[ \int \frac {1}{e^6 x} \, dx=\frac {\log (x)}{e^6} \]

[In]

Int[1/(E^6*x),x]

[Out]

Log[x]/E^6

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}& = \frac {\int \frac {1}{x} \, dx}{e^6} \\ & = \frac {\log (x)}{e^6} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.60 \[ \int \frac {1}{e^6 x} \, dx=\frac {\log (x)}{e^6} \]

[In]

Integrate[1/(E^6*x),x]

[Out]

Log[x]/E^6

Maple [A] (verified)

Time = 0.14 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.60

method	result	size
risch	\({\mathrm e}^{-6} \ln \left (x \right )\)	\(6\)
default	\({\mathrm e}^{-6} \ln \left (x \right )\)	\(8\)
norman	\({\mathrm e}^{-6} \ln \left (x \right )\)	\(8\)
parallelrisch	\({\mathrm e}^{-6} \ln \left (x \right )\)	\(8\)

[In]

int(1/x/exp(6),x,method=_RETURNVERBOSE)

[Out]

exp(-6)*ln(x)

Fricas [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.50 \[ \int \frac {1}{e^6 x} \, dx=e^{\left (-6\right )} \log \left (x\right ) \]

[In]

integrate(1/x/exp(6),x, algorithm="fricas")

[Out]

e^(-6)*log(x)

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.50 \[ \int \frac {1}{e^6 x} \, dx=\frac {\log {\left (x \right )}}{e^{6}} \]

[In]

integrate(1/x/exp(6),x)

[Out]

exp(-6)*log(x)

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.50 \[ \int \frac {1}{e^6 x} \, dx=e^{\left (-6\right )} \log \left (x\right ) \]

[In]

integrate(1/x/exp(6),x, algorithm="maxima")

[Out]

e^(-6)*log(x)

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.60 \[ \int \frac {1}{e^6 x} \, dx=e^{\left (-6\right )} \log \left ({\left | x \right |}\right ) \]

[In]

integrate(1/x/exp(6),x, algorithm="giac")

[Out]

e^(-6)*log(abs(x))

Mupad [B] (verification not implemented)

Time = 15.06 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.50 \[ \int \frac {1}{e^6 x} \, dx={\mathrm {e}}^{-6}\,\ln \left (x\right ) \]

[In]

int(exp(-6)/x,x)

[Out]

exp(-6)*log(x)