3.41.26 \(\int \frac {19}{32 x} \, dx\)

Optimal. Leaf size=13 \[ \frac {x+\frac {19}{32} x \log (x)}{x} \]

________________________________________________________________________________________

Rubi [A]  time = 0.00, antiderivative size = 6, normalized size of antiderivative = 0.46, number of steps used = 2, number of rules used = 2, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.286, Rules used = {12, 29} \begin {gather*} \frac {19 \log (x)}{32} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[19/(32*x),x]

[Out]

(19*Log[x])/32

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 {gather*} \begin {aligned} \text {integral} &=\frac {19}{32} \int \frac {1}{x} \, dx\\ &=\frac {19 \log (x)}{32}\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.00, size = 6, normalized size = 0.46 \begin {gather*} \frac {19 \log (x)}{32} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[19/(32*x),x]

[Out]

(19*Log[x])/32

________________________________________________________________________________________

fricas [A]  time = 0.87, size = 4, normalized size = 0.31 \begin {gather*} \frac {19}{32} \, \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(19/32/x,x, algorithm="fricas")

[Out]

19/32*log(x)

________________________________________________________________________________________

giac [A]  time = 0.21, size = 5, normalized size = 0.38 \begin {gather*} \frac {19}{32} \, \log \left ({\left | x \right |}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(19/32/x,x, algorithm="giac")

[Out]

19/32*log(abs(x))

________________________________________________________________________________________

maple [A]  time = 0.02, size = 5, normalized size = 0.38

method	result	size
default	\(\frac {19 \ln \relax (x )}{32}\)	\(5\)
norman	\(\frac {19 \ln \relax (x )}{32}\)	\(5\)
risch	\(\frac {19 \ln \relax (x )}{32}\)	\(5\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(19/32/x,x,method=_RETURNVERBOSE)

[Out]

19/32*ln(x)

________________________________________________________________________________________

maxima [A]  time = 0.34, size = 4, normalized size = 0.31 \begin {gather*} \frac {19}{32} \, \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(19/32/x,x, algorithm="maxima")

[Out]

19/32*log(x)

________________________________________________________________________________________

mupad [B]  time = 0.09, size = 4, normalized size = 0.31 \begin {gather*} \frac {19\,\ln \relax (x)}{32} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(19/(32*x),x)

[Out]

(19*log(x))/32

________________________________________________________________________________________

sympy [A]  time = 0.05, size = 5, normalized size = 0.38 \begin {gather*} \frac {19 \log {\relax (x )}}{32} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(19/32/x,x)

[Out]

19*log(x)/32

________________________________________________________________________________________