3.33.54 $\int \frac{1}{x}dx$

Optimal. Leaf size=12 $$\log \left(2(1+e^9+e^{16})x\right)$$

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Rubi [A]  time = 0.00, antiderivative size = 2, normalized size of antiderivative = 0.17, number of steps used = 1, number of rules used = 1, integrand size = 3, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.333, Rules used = {29} $$\begin{array}{c}\log (x)\end{array}$$

Antiderivative was successfully verified.

[In]

Int[x^(-1),x]

[Out]

Log[x]

Rule 29

Int[(x_)^(-1), x_Symbol] :> Simp[Log[x], x]

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\log (x)\end{array}\end{array}$$

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

Antiderivative was successfully verified.

[In]

Integrate[x^(-1),x]

[Out]

Log[x]

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x,x, algorithm="fricas")

[Out]

log(x)

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giac [A]  time = 0.20, size = 3, normalized size = 0.25 $$\begin{array}{c}\log \left(\left|x\right|\right)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x,x, algorithm="giac")

[Out]

log(abs(x))

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maple [A]  time = 0.01, size = 3, normalized size = 0.25

method	result	size
default	$\ln (x)$	$3$
norman	$\ln (x)$	$3$
risch	$\ln (x)$	$3$

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

ln(x)

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maxima [A]  time = 0.33, size = 2, normalized size = 0.17 $$\begin{array}{c}\log (x)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x,x, algorithm="maxima")

[Out]

log(x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/x,x)

[Out]

log(x)

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sympy [A]  time = 0.06, size = 2, normalized size = 0.17 $$\begin{array}{c}\log (x)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x,x)

[Out]

log(x)

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