3.67.77 $\int \frac{x+\log (3)}{x}dx$

Optimal. Leaf size=19 $$x-\log (3)(2+{(2+e^5)}^2-\log (x))$$

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Rubi [A]  time = 0.00, antiderivative size = 7, normalized size of antiderivative = 0.37, number of steps used = 2, number of rules used = 1, integrand size = 8, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.125, Rules used = {43} $$\begin{array}{c}x+\log (3)\log (x)\end{array}$$

Antiderivative was successfully verified.

[In]

Int[(x + Log[3])/x,x]

[Out]

x + Log[3]*Log[x]

Rule 43

Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.), x_Symbol] :> Int[ExpandIntegrand[(a + b*x)^m*(c + d
*x)^n, x], x] /; FreeQ[{a, b, c, d, n}, x] && NeQ[b*c - a*d, 0] && IGtQ[m, 0] && ( !IntegerQ[n] || (EqQ[c, 0]
&& LeQ[7*m + 4*n + 4, 0]) || LtQ[9*m + 5*(n + 1), 0] || GtQ[m + n + 2, 0])

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\int (1+\frac{\log (3)}{x})dx\\ & =x+\log (3)\log (x)\end{array}\end{array}$$

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Mathematica [A]  time = 0.00, size = 7, normalized size = 0.37 $$\begin{array}{c}x+\log (3)\log (x)\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(x + Log[3])/x,x]

[Out]

x + Log[3]*Log[x]

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fricas [A]  time = 0.47, size = 7, normalized size = 0.37 $$\begin{array}{c}\log (3)\log (x)+x\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((log(3)+x)/x,x, algorithm="fricas")

[Out]

log(3)*log(x) + x

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giac [A]  time = 0.19, size = 8, normalized size = 0.42 $$\begin{array}{c}\log (3)\log \left(\left|x\right|\right)+x\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((log(3)+x)/x,x, algorithm="giac")

[Out]

log(3)*log(abs(x)) + x

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maple [A]  time = 0.02, size = 8, normalized size = 0.42

method	result	size
default	$x+\ln (3)\ln (x)$	$8$
norman	$x+\ln (3)\ln (x)$	$8$
risch	$x+\ln (3)\ln (x)$	$8$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((ln(3)+x)/x,x,method=_RETURNVERBOSE)

[Out]

x+ln(3)*ln(x)

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maxima [A]  time = 0.36, size = 7, normalized size = 0.37 $$\begin{array}{c}\log (3)\log (x)+x\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((log(3)+x)/x,x, algorithm="maxima")

[Out]

log(3)*log(x) + x

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mupad [B]  time = 0.02, size = 7, normalized size = 0.37 $$\begin{array}{c}x+\ln (3)\ln (x)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((x + log(3))/x,x)

[Out]

x + log(3)*log(x)

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sympy [A]  time = 0.10, size = 7, normalized size = 0.37 $$\begin{array}{c}x+\log (3)\log (x)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((ln(3)+x)/x,x)

[Out]

x + log(3)*log(x)

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