\(\int \frac {x+\log (3)}{x} \, dx\) [6677]

Optimal result

Integrand size = 8, antiderivative size = 19 \[ \int \frac {x+\log (3)}{x} \, dx=x-\log (3) \left (2+\left (2+e^5\right )^2-\log (x)\right ) \]

[Out]

x-(2+(exp(5)+2)^2-ln(x))*ln(3)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.37, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {45} \[ \int \frac {x+\log (3)}{x} \, dx=x+\log (3) \log (x) \]

[In]

Int[(x + Log[3])/x,x]

[Out]

x + Log[3]*Log[x]

Rule 45

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{align*} \text {integral}& = \int \left (1+\frac {\log (3)}{x}\right ) \, dx \\ & = x+\log (3) \log (x) \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.37 \[ \int \frac {x+\log (3)}{x} \, dx=x+\log (3) \log (x) \]

[In]

Integrate[(x + Log[3])/x,x]

[Out]

x + Log[3]*Log[x]

Maple [A] (verified)

Time = 0.10 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.42

method	result	size
default	\(x +\ln \left (3\right ) \ln \left (x \right )\)	\(8\)
norman	\(x +\ln \left (3\right ) \ln \left (x \right )\)	\(8\)
risch	\(x +\ln \left (3\right ) \ln \left (x \right )\)	\(8\)
parallelrisch	\(x +\ln \left (3\right ) \ln \left (x \right )\)	\(8\)

[In]

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

[Out]

x+ln(3)*ln(x)

Fricas [A] (verification not implemented)

none

Time = 0.40 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.37 \[ \int \frac {x+\log (3)}{x} \, dx=\log \left (3\right ) \log \left (x\right ) + x \]

[In]

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

[Out]

log(3)*log(x) + x

Sympy [A] (verification not implemented)

Time = 0.04 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.37 \[ \int \frac {x+\log (3)}{x} \, dx=x + \log {\left (3 \right )} \log {\left (x \right )} \]

[In]

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

[Out]

x + log(3)*log(x)

Maxima [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.37 \[ \int \frac {x+\log (3)}{x} \, dx=\log \left (3\right ) \log \left (x\right ) + x \]

[In]

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

[Out]

log(3)*log(x) + x

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.42 \[ \int \frac {x+\log (3)}{x} \, dx=\log \left (3\right ) \log \left ({\left | x \right |}\right ) + x \]

[In]

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

[Out]

log(3)*log(abs(x)) + x

Mupad [B] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.37 \[ \int \frac {x+\log (3)}{x} \, dx=x+\ln \left (3\right )\,\ln \left (x\right ) \]

[In]

int((x + log(3))/x,x)

[Out]

x + log(3)*log(x)