3.33.97 $\int \frac{2}{x}dx$

Optimal. Leaf size=23 $$\log \left(x^2(3-\frac{2}{-3+\frac{1}{e^{15/4}}}+e^3+\log (4))\right)$$

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Rubi [A]  time = 0.00, antiderivative size = 4, normalized size of antiderivative = 0.17, number of steps used = 2, number of rules used = 2, integrand size = 5, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.400, Rules used = {12, 29} $$\begin{array}{c}2\log (x)\end{array}$$

Antiderivative was successfully verified.

[In]

Int[2/x,x]

[Out]

2*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

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =2\int \frac{1}{x}dx\\ & =2\log (x)\end{array}\end{array}$$

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Mathematica [A]  time = 0.00, size = 4, normalized size = 0.17 $$\begin{array}{c}2\log (x)\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[2/x,x]

[Out]

2*Log[x]

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fricas [A]  time = 0.60, size = 4, normalized size = 0.17 $$\begin{array}{c}2\log (x)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2/x,x, algorithm="fricas")

[Out]

2*log(x)

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giac [A]  time = 0.33, size = 5, normalized size = 0.22 $$\begin{array}{c}2\log \left(\left|x\right|\right)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2/x,x, algorithm="giac")

[Out]

2*log(abs(x))

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maple [A]  time = 0.01, size = 5, normalized size = 0.22

method	result	size
default	$2\ln (x)$	$5$
norman	$2\ln (x)$	$5$
risch	$2\ln (x)$	$5$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2/x,x,method=_RETURNVERBOSE)

[Out]

2*ln(x)

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maxima [A]  time = 0.69, size = 4, normalized size = 0.17 $$\begin{array}{c}2\log (x)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2/x,x, algorithm="maxima")

[Out]

2*log(x)

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mupad [B]  time = 0.01, size = 4, normalized size = 0.17 $$\begin{array}{c}2\ln (x)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2/x,x)

[Out]

2*log(x)

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sympy [A]  time = 0.06, size = 3, normalized size = 0.13 $$\begin{array}{c}2\log (x)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2/x,x)

[Out]

2*log(x)

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