\(\int \frac {1}{\log (5)} \, dx\) [3231]

Optimal result

Integrand size = 4, antiderivative size = 13 \[ \int \frac {1}{\log (5)} \, dx=2-\frac {295-x}{\log (5)} \]

[Out]

2-(295-x)/ln(5)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.46, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {8} \[ \int \frac {1}{\log (5)} \, dx=\frac {x}{\log (5)} \]

[In]

Int[Log[5]^(-1),x]

[Out]

x/Log[5]

Rule 8

Int[a_, x_Symbol] :> Simp[a*x, x] /; FreeQ[a, x]

Rubi steps \begin{align*} \text {integral}& = \frac {x}{\log (5)} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.46 \[ \int \frac {1}{\log (5)} \, dx=\frac {x}{\log (5)} \]

[In]

Integrate[Log[5]^(-1),x]

[Out]

x/Log[5]

Maple [A] (verified)

Time = 0.22 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.54

method	result	size
default	\(\frac {x}{\ln \left (5\right )}\)	\(7\)
norman	\(\frac {x}{\ln \left (5\right )}\)	\(7\)
risch	\(\frac {x}{\ln \left (5\right )}\)	\(7\)
parallelrisch	\(\frac {x}{\ln \left (5\right )}\)	\(7\)

[In]

int(1/ln(5),x,method=_RETURNVERBOSE)

[Out]

x/ln(5)

Fricas [A] (verification not implemented)

none

Time = 0.24 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.46 \[ \int \frac {1}{\log (5)} \, dx=\frac {x}{\log \left (5\right )} \]

[In]

integrate(1/log(5),x, algorithm="fricas")

[Out]

x/log(5)

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 3, normalized size of antiderivative = 0.23 \[ \int \frac {1}{\log (5)} \, dx=\frac {x}{\log {\left (5 \right )}} \]

[In]

integrate(1/ln(5),x)

[Out]

x/log(5)

Maxima [A] (verification not implemented)

none

Time = 0.18 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.46 \[ \int \frac {1}{\log (5)} \, dx=\frac {x}{\log \left (5\right )} \]

[In]

integrate(1/log(5),x, algorithm="maxima")

[Out]

x/log(5)

Giac [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.46 \[ \int \frac {1}{\log (5)} \, dx=\frac {x}{\log \left (5\right )} \]

[In]

integrate(1/log(5),x, algorithm="giac")

[Out]

x/log(5)

Mupad [B] (verification not implemented)

Time = 0.00 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.46 \[ \int \frac {1}{\log (5)} \, dx=\frac {x}{\ln \left (5\right )} \]

[In]

int(1/log(5),x)

[Out]

x/log(5)