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

Optimal. Leaf size=13 \[ 2-\frac {295-x}{\log (5)} \]

[Out]

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

________________________________________________________________________________________

Rubi [A]
time = 0.00, antiderivative size = 6, normalized size of antiderivative = 0.46, number of steps used = 1, number of rules used = 1, integrand size = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {8} \begin {gather*} \frac {x}{\log (5)} \end {gather*}

Antiderivative was successfully verified.

[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 {gather*} \begin {aligned} \text {integral} &=\frac {x}{\log (5)}\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]
time = 0.00, size = 6, normalized size = 0.46 \begin {gather*} \frac {x}{\log (5)} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

x/Log[5]

________________________________________________________________________________________

Maple [A]
time = 0.10, size = 7, normalized size = 0.54

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x/ln(5)

________________________________________________________________________________________

Maxima [A]
time = 0.26, size = 6, normalized size = 0.46 \begin {gather*} \frac {x}{\log \left (5\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x/log(5)

________________________________________________________________________________________

Fricas [A]
time = 0.39, size = 6, normalized size = 0.46 \begin {gather*} \frac {x}{\log \left (5\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x/log(5)

________________________________________________________________________________________

Sympy [A]
time = 0.00, size = 3, normalized size = 0.23 \begin {gather*} \frac {x}{\log {\left (5 \right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/ln(5),x)

[Out]

x/log(5)

________________________________________________________________________________________

Giac [A]
time = 0.39, size = 6, normalized size = 0.46 \begin {gather*} \frac {x}{\log \left (5\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x/log(5)

________________________________________________________________________________________

Mupad [B]
time = 0.00, size = 6, normalized size = 0.46 \begin {gather*} \frac {x}{\ln \left (5\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/log(5),x)

[Out]

x/log(5)

________________________________________________________________________________________