\(\int \frac {1}{x} \, dx\) [6714]

Optimal result

Integrand size = 3, antiderivative size = 6 \[ \int \frac {1}{x} \, dx=\log (x)+\log (\log (3)) \]

[Out]

ln(ln(3))+ln(x)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 2, normalized size of antiderivative = 0.33, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.333, Rules used = {29} \[ \int \frac {1}{x} \, dx=\log (x) \]

[In]

Int[x^(-1),x]

[Out]

Log[x]

Rule 29

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

Rubi steps \begin{align*} \text {integral}& = \log (x) \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 2, normalized size of antiderivative = 0.33 \[ \int \frac {1}{x} \, dx=\log (x) \]

[In]

Integrate[x^(-1),x]

[Out]

Log[x]

Maple [A] (verified)

Time = 0.02 (sec) , antiderivative size = 3, normalized size of antiderivative = 0.50

method	result	size
default	\(\ln \left (x \right )\)	\(3\)
norman	\(\ln \left (x \right )\)	\(3\)
risch	\(\ln \left (x \right )\)	\(3\)
parallelrisch	\(\ln \left (x \right )\)	\(3\)

[In]

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

[Out]

ln(x)

Fricas [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 2, normalized size of antiderivative = 0.33 \[ \int \frac {1}{x} \, dx=\log \left (x\right ) \]

[In]

integrate(1/x,x, algorithm="fricas")

[Out]

log(x)

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 2, normalized size of antiderivative = 0.33 \[ \int \frac {1}{x} \, dx=\log {\left (x \right )} \]

[In]

integrate(1/x,x)

[Out]

log(x)

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 2, normalized size of antiderivative = 0.33 \[ \int \frac {1}{x} \, dx=\log \left (x\right ) \]

[In]

integrate(1/x,x, algorithm="maxima")

[Out]

log(x)

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 3, normalized size of antiderivative = 0.50 \[ \int \frac {1}{x} \, dx=\log \left ({\left | x \right |}\right ) \]

[In]

integrate(1/x,x, algorithm="giac")

[Out]

log(abs(x))

Mupad [B] (verification not implemented)

Time = 0.00 (sec) , antiderivative size = 2, normalized size of antiderivative = 0.33 \[ \int \frac {1}{x} \, dx=\ln \left (x\right ) \]

[In]

int(1/x,x)

[Out]

log(x)