3.17.63 $\int -\frac{1}{x}dx$

Optimal. Leaf size=9 $$\log \left(\frac{1944}{e^{5}x}\right)$$

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Rubi [A]  time = 0.00, antiderivative size = 4, normalized size of antiderivative = 0.44, number of steps used = 1, number of rules used = 1, integrand size = 5, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.200, 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 = 4, normalized size = 0.44 $$\begin{array}{c}-\log (x)\end{array}$$

Antiderivative was successfully verified.

[In]

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

[Out]

-Log[x]

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fricas [A]  time = 0.55, size = 4, normalized size = 0.44 $$\begin{array}{c}-\log (x)\end{array}$$

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 = 0.43, size = 5, normalized size = 0.56 $$\begin{array}{c}-\log \left(\left|x\right|\right)\end{array}$$

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 = 5, normalized size = 0.56

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

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 = 0.56, size = 4, normalized size = 0.44 $$\begin{array}{c}-\log (x)\end{array}$$

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 = 4, normalized size = 0.44 $$\begin{array}{c}-\ln (x)\end{array}$$

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 = 0.05, size = 3, normalized size = 0.33 $$\begin{array}{c}-\log (x)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/x,x)

[Out]

-log(x)

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