3.41.26 $\int \frac{19}{32x}dx$

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} $$\begin{array}{c}\frac{19\log (x)}{32}\end{array}$$

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

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\frac{19}{32}\int \frac{1}{x}dx\\ & =\frac{19\log (x)}{32}\end{array}\end{array}$$

________________________________________________________________________________________

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

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 $$\begin{array}{c}\frac{19}{32}\log (x)\end{array}$$

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 $$\begin{array}{c}\frac{19}{32}\log \left(\left|x\right|\right)\end{array}$$

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	$\frac{19\ln (x)}{32}$	$5$
norman	$\frac{19\ln (x)}{32}$	$5$
risch	$\frac{19\ln (x)}{32}$	$5$

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 $$\begin{array}{c}\frac{19}{32}\log (x)\end{array}$$

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 $$\begin{array}{c}\frac{19\ln (x)}{32}\end{array}$$

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 $$\begin{array}{c}\frac{19\log (x)}{32}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(19/32/x,x)

[Out]

19*log(x)/32

________________________________________________________________________________________