\(\int -\frac {6}{x} \, dx\) [2754]

Optimal result

Integrand size = 5, antiderivative size = 16 \[ \int -\frac {6}{x} \, dx=5 \left (-9+\frac {1}{5} \left (\frac {4}{5}-6 \log (x)\right )\right ) \]

[Out]

-221/5-6*ln(x)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 4, normalized size of antiderivative = 0.25, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.400, Rules used = {12, 29} \[ \int -\frac {6}{x} \, dx=-6 \log (x) \]

[In]

Int[-6/x,x]

[Out]

-6*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{align*} \text {integral}& = -\left (6 \int \frac {1}{x} \, dx\right ) \\ & = -6 \log (x) \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 4, normalized size of antiderivative = 0.25 \[ \int -\frac {6}{x} \, dx=-6 \log (x) \]

[In]

Integrate[-6/x,x]

[Out]

-6*Log[x]

Maple [A] (verified)

Time = 0.01 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.31

method	result	size
default	\(-6 \ln \left (x \right )\)	\(5\)
norman	\(-6 \ln \left (x \right )\)	\(5\)
risch	\(-6 \ln \left (x \right )\)	\(5\)
parallelrisch	\(-6 \ln \left (x \right )\)	\(5\)

[In]

int(-6/x,x,method=_RETURNVERBOSE)

[Out]

-6*ln(x)

Fricas [A] (verification not implemented)

none

Time = 0.23 (sec) , antiderivative size = 4, normalized size of antiderivative = 0.25 \[ \int -\frac {6}{x} \, dx=-6 \, \log \left (x\right ) \]

[In]

integrate(-6/x,x, algorithm="fricas")

[Out]

-6*log(x)

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.31 \[ \int -\frac {6}{x} \, dx=- 6 \log {\left (x \right )} \]

[In]

integrate(-6/x,x)

[Out]

-6*log(x)

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 4, normalized size of antiderivative = 0.25 \[ \int -\frac {6}{x} \, dx=-6 \, \log \left (x\right ) \]

[In]

integrate(-6/x,x, algorithm="maxima")

[Out]

-6*log(x)

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.31 \[ \int -\frac {6}{x} \, dx=-6 \, \log \left ({\left | x \right |}\right ) \]

[In]

integrate(-6/x,x, algorithm="giac")

[Out]

-6*log(abs(x))

Mupad [B] (verification not implemented)

Time = 0.01 (sec) , antiderivative size = 4, normalized size of antiderivative = 0.25 \[ \int -\frac {6}{x} \, dx=-6\,\ln \left (x\right ) \]

[In]

int(-6/x,x)

[Out]

-6*log(x)