\(\int \frac {e^2}{3 x} \, dx\) [9892]

Optimal result

Integrand size = 10, antiderivative size = 11 \[ \int \frac {e^2}{3 x} \, dx=-14+\frac {1}{3} e^2 \log (x) \]

[Out]

-14+1/3*exp(2)*ln(x)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.82, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {12, 29} \[ \int \frac {e^2}{3 x} \, dx=\frac {1}{3} e^2 \log (x) \]

[In]

Int[E^2/(3*x),x]

[Out]

(E^2*Log[x])/3

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 {1}{3} e^2 \int \frac {1}{x} \, dx \\ & = \frac {1}{3} e^2 \log (x) \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.82 \[ \int \frac {e^2}{3 x} \, dx=\frac {1}{3} e^2 \log (x) \]

[In]

Integrate[E^2/(3*x),x]

[Out]

(E^2*Log[x])/3

Maple [A] (verified)

Time = 0.09 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.64

method	result	size
default	\(\frac {{\mathrm e}^{2} \ln \left (x \right )}{3}\)	\(7\)
norman	\(\frac {{\mathrm e}^{2} \ln \left (x \right )}{3}\)	\(7\)
risch	\(\frac {{\mathrm e}^{2} \ln \left (x \right )}{3}\)	\(7\)
parallelrisch	\(\frac {{\mathrm e}^{2} \ln \left (x \right )}{3}\)	\(7\)

[In]

int(1/3*exp(2)/x,x,method=_RETURNVERBOSE)

[Out]

1/3*exp(2)*ln(x)

Fricas [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.55 \[ \int \frac {e^2}{3 x} \, dx=\frac {1}{3} \, e^{2} \log \left (x\right ) \]

[In]

integrate(1/3*exp(2)/x,x, algorithm="fricas")

[Out]

1/3*e^2*log(x)

Sympy [A] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.64 \[ \int \frac {e^2}{3 x} \, dx=\frac {e^{2} \log {\left (x \right )}}{3} \]

[In]

integrate(1/3*exp(2)/x,x)

[Out]

exp(2)*log(x)/3

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.55 \[ \int \frac {e^2}{3 x} \, dx=\frac {1}{3} \, e^{2} \log \left (x\right ) \]

[In]

integrate(1/3*exp(2)/x,x, algorithm="maxima")

[Out]

1/3*e^2*log(x)

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.64 \[ \int \frac {e^2}{3 x} \, dx=\frac {1}{3} \, e^{2} \log \left ({\left | x \right |}\right ) \]

[In]

integrate(1/3*exp(2)/x,x, algorithm="giac")

[Out]

1/3*e^2*log(abs(x))

Mupad [B] (verification not implemented)

Time = 0.04 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.55 \[ \int \frac {e^2}{3 x} \, dx=\frac {{\mathrm {e}}^2\,\ln \left (x\right )}{3} \]

[In]

int(exp(2)/(3*x),x)

[Out]

(exp(2)*log(x))/3