3.17.75 $\int -\frac{1}{3x}dx$

Optimal. Leaf size=10 $$\frac{1}{3}(1-\log (x))$$

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Rubi [A]  time = 0.00, antiderivative size = 6, normalized size of antiderivative = 0.60, 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} $$\begin{array}{c}-\frac{\log (x)}{3}\end{array}$$

Antiderivative was successfully verified.

[In]

Int[-1/3*1/x,x]

[Out]

-1/3*Log[x]

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

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =-(\frac{1}{3}\int \frac{1}{x}dx)\\ & =-\frac{\log (x)}{3}\end{array}\end{array}$$

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Mathematica [A]  time = 0.00, size = 6, normalized size = 0.60 $$\begin{array}{c}-\frac{\log (x)}{3}\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[-1/3*1/x,x]

[Out]

-1/3*Log[x]

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fricas [A]  time = 0.72, size = 4, normalized size = 0.40 $$\begin{array}{c}-\frac{1}{3}\log (x)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/3/x,x, algorithm="fricas")

[Out]

-1/3*log(x)

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giac [A]  time = 0.21, size = 5, normalized size = 0.50 $$\begin{array}{c}-\frac{1}{3}\log \left(\left|x\right|\right)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/3/x,x, algorithm="giac")

[Out]

-1/3*log(abs(x))

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maple [A]  time = 0.01, size = 5, normalized size = 0.50

method	result	size
default	$-\frac{\ln (x)}{3}$	$5$
norman	$-\frac{\ln (x)}{3}$	$5$
risch	$-\frac{\ln (x)}{3}$	$5$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-1/3/x,x,method=_RETURNVERBOSE)

[Out]

-1/3*ln(x)

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maxima [A]  time = 0.55, size = 4, normalized size = 0.40 $$\begin{array}{c}-\frac{1}{3}\log (x)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/3/x,x, algorithm="maxima")

[Out]

-1/3*log(x)

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mupad [B]  time = 1.08, size = 4, normalized size = 0.40 $$\begin{array}{c}-\frac{\ln (x)}{3}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-1/(3*x),x)

[Out]

-log(x)/3

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sympy [A]  time = 0.06, size = 5, normalized size = 0.50 $$\begin{array}{c}-\frac{\log (x)}{3}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/3/x,x)

[Out]

-log(x)/3

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