3.3.27 \(\int \frac {1}{4 x} \, dx\)

Optimal. Leaf size=18 \[ -5+e^2+i \pi +\log (20)+\frac {\log (x)}{4} \]

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Rubi [A]  time = 0.00, antiderivative size = 6, normalized size of antiderivative = 0.33, number of steps used = 2, number of rules used = 2, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.286, Rules used = {12, 29} \begin {gather*} \frac {\log (x)}{4} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[1/(4*x),x]

[Out]

Log[x]/4

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 {gather*} \begin {aligned} \text {integral} &=\frac {1}{4} \int \frac {1}{x} \, dx\\ &=\frac {\log (x)}{4}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 6, normalized size = 0.33 \begin {gather*} \frac {\log (x)}{4} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[1/(4*x),x]

[Out]

Log[x]/4

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fricas [A]  time = 0.77, size = 4, normalized size = 0.22 \begin {gather*} \frac {1}{4} \, \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/4/x,x, algorithm="fricas")

[Out]

1/4*log(x)

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giac [A]  time = 0.33, size = 5, normalized size = 0.28 \begin {gather*} \frac {1}{4} \, \log \left ({\left | x \right |}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/4/x,x, algorithm="giac")

[Out]

1/4*log(abs(x))

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maple [A]  time = 0.01, size = 5, normalized size = 0.28

method	result	size
default	\(\frac {\ln \relax (x )}{4}\)	\(5\)
norman	\(\frac {\ln \relax (x )}{4}\)	\(5\)
risch	\(\frac {\ln \relax (x )}{4}\)	\(5\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/4/x,x,method=_RETURNVERBOSE)

[Out]

1/4*ln(x)

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maxima [A]  time = 0.49, size = 4, normalized size = 0.22 \begin {gather*} \frac {1}{4} \, \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/4/x,x, algorithm="maxima")

[Out]

1/4*log(x)

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mupad [B]  time = 0.29, size = 4, normalized size = 0.22 \begin {gather*} \frac {\ln \relax (x)}{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(4*x),x)

[Out]

log(x)/4

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sympy [A]  time = 0.06, size = 3, normalized size = 0.17 \begin {gather*} \frac {\log {\relax (x )}}{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/4/x,x)

[Out]

log(x)/4

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