3.36.32 \(\int \frac {1}{5+\log (5)} \, dx\) [3532]

Optimal. Leaf size=27 \[ e-\left (-\frac {1}{2}+x\right )^2-x+x^2+\log (3)+\frac {x}{5+\log (5)} \]

[Out]

ln(3)+x^2+x/(5+ln(5))-x+exp(1)-(x-1/2)^2

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Rubi [A]
time = 0.00, antiderivative size = 8, normalized size of antiderivative = 0.30, number of steps used = 1, number of rules used = 1, integrand size = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {8} \begin {gather*} \frac {x}{5+\log (5)} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(5 + Log[5])^(-1),x]

[Out]

x/(5 + 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}{5+\log (5)}\\ \end {aligned} \end {gather*}

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Mathematica [A]
time = 0.00, size = 8, normalized size = 0.30 \begin {gather*} \frac {x}{5+\log (5)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(5 + Log[5])^(-1),x]

[Out]

x/(5 + Log[5])

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Maple [A]
time = 0.20, size = 9, normalized size = 0.33

method	result	size
default	\(\frac {x}{5+\ln \left (5\right )}\)	\(9\)
norman	\(\frac {x}{5+\ln \left (5\right )}\)	\(9\)
risch	\(\frac {x}{5+\ln \left (5\right )}\)	\(9\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x/(5+ln(5))

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Maxima [A]
time = 0.26, size = 8, normalized size = 0.30 \begin {gather*} \frac {x}{\log \left (5\right ) + 5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x/(log(5) + 5)

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Fricas [A]
time = 0.34, size = 8, normalized size = 0.30 \begin {gather*} \frac {x}{\log \left (5\right ) + 5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x/(log(5) + 5)

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Sympy [A]
time = 0.00, size = 5, normalized size = 0.19 \begin {gather*} \frac {x}{\log {\left (5 \right )} + 5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(5+ln(5)),x)

[Out]

x/(log(5) + 5)

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Giac [A]
time = 0.40, size = 8, normalized size = 0.30 \begin {gather*} \frac {x}{\log \left (5\right ) + 5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x/(log(5) + 5)

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Mupad [B]
time = 0.00, size = 8, normalized size = 0.30 \begin {gather*} \frac {x}{\ln \left (5\right )+5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(log(5) + 5),x)

[Out]

x/(log(5) + 5)

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