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

Optimal. Leaf size=19 \[ x-\log (3) \left (2+\left (2+e^5\right )^2-\log (x)\right ) \]

________________________________________________________________________________________

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 {gather*} x+\log (3) \log (x) \end {gather*}

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

________________________________________________________________________________________

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

Antiderivative was successfully verified.

[In]

Integrate[(x + Log[3])/x,x]

[Out]

x + Log[3]*Log[x]

________________________________________________________________________________________

fricas [A]  time = 0.47, size = 7, normalized size = 0.37 \begin {gather*} \log \relax (3) \log \relax (x) + x \end {gather*}

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

________________________________________________________________________________________

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

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

________________________________________________________________________________________

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

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

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)

________________________________________________________________________________________

maxima [A]  time = 0.36, size = 7, normalized size = 0.37 \begin {gather*} \log \relax (3) \log \relax (x) + x \end {gather*}

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

________________________________________________________________________________________

mupad [B]  time = 0.02, size = 7, normalized size = 0.37 \begin {gather*} x+\ln \relax (3)\,\ln \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((x + log(3))/x,x)

[Out]

x + log(3)*log(x)

________________________________________________________________________________________

sympy [A]  time = 0.10, size = 7, normalized size = 0.37 \begin {gather*} x + \log {\relax (3 )} \log {\relax (x )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x + log(3)*log(x)

________________________________________________________________________________________