3.44.46 \(\int -\frac {1}{\log (4)} \, dx\) [4346]

Optimal. Leaf size=12 \[ \frac {\frac {5}{4}-x}{\log (4)} \]

[Out]

1/2*(5/4-x)/ln(2)

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Rubi [A]
time = 0.00, antiderivative size = 7, normalized size of antiderivative = 0.58, 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}{\log (4)} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-Log[4]^(-1),x]

[Out]

-(x/Log[4])

Rule 8

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

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-\frac {x}{\log (4)}\\ \end {aligned} \end {gather*}

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Mathematica [A]
time = 0.00, size = 7, normalized size = 0.58 \begin {gather*} -\frac {x}{\log (4)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-Log[4]^(-1),x]

[Out]

-(x/Log[4])

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Maple [A]
time = 0.08, size = 8, normalized size = 0.67

method	result	size
default	\(-\frac {x}{2 \ln \left (2\right )}\)	\(8\)
norman	\(-\frac {x}{2 \ln \left (2\right )}\)	\(8\)
risch	\(-\frac {x}{2 \ln \left (2\right )}\)	\(8\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-1/2/ln(2),x,method=_RETURNVERBOSE)

[Out]

-1/2*x/ln(2)

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Maxima [A]
time = 0.28, size = 7, normalized size = 0.58 \begin {gather*} -\frac {x}{2 \, \log \left (2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/2/log(2),x, algorithm="maxima")

[Out]

-1/2*x/log(2)

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Fricas [A]
time = 0.35, size = 7, normalized size = 0.58 \begin {gather*} -\frac {x}{2 \, \log \left (2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/2/log(2),x, algorithm="fricas")

[Out]

-1/2*x/log(2)

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Sympy [A]
time = 0.00, size = 7, normalized size = 0.58 \begin {gather*} - \frac {x}{2 \log {\left (2 \right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/2/ln(2),x)

[Out]

-x/(2*log(2))

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Giac [A]
time = 0.42, size = 7, normalized size = 0.58 \begin {gather*} -\frac {x}{2 \, \log \left (2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/2/log(2),x, algorithm="giac")

[Out]

-1/2*x/log(2)

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Mupad [B]
time = 0.00, size = 7, normalized size = 0.58 \begin {gather*} -\frac {x}{2\,\ln \left (2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-1/(2*log(2)),x)

[Out]

-x/(2*log(2))

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