3.90.94 \(\int \frac {x+e^4 \log ^2(3)}{x^2} \, dx\)

Optimal. Leaf size=17 \[ \log \left (e^{-\frac {e^4 \log ^2(3)}{x}} x\right ) \]

________________________________________________________________________________________

Rubi [A]  time = 0.01, antiderivative size = 15, normalized size of antiderivative = 0.88, number of steps used = 2, number of rules used = 1, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {43} \begin {gather*} \log (x)-\frac {e^4 \log ^2(3)}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(x + E^4*Log[3]^2)/x^2,x]

[Out]

-((E^4*Log[3]^2)/x) + 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 (\frac {1}{x}+\frac {e^4 \log ^2(3)}{x^2}\right ) \, dx\\ &=-\frac {e^4 \log ^2(3)}{x}+\log (x)\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.00, size = 15, normalized size = 0.88 \begin {gather*} -\frac {e^4 \log ^2(3)}{x}+\log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(x + E^4*Log[3]^2)/x^2,x]

[Out]

-((E^4*Log[3]^2)/x) + Log[x]

________________________________________________________________________________________

fricas [A]  time = 0.42, size = 18, normalized size = 1.06 \begin {gather*} -\frac {e^{4} \log \relax (3)^{2} - x \log \relax (x)}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((exp(4)*log(3)^2+x)/x^2,x, algorithm="fricas")

[Out]

-(e^4*log(3)^2 - x*log(x))/x

________________________________________________________________________________________

giac [A]  time = 0.13, size = 15, normalized size = 0.88 \begin {gather*} -\frac {e^{4} \log \relax (3)^{2}}{x} + \log \left ({\left | x \right |}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((exp(4)*log(3)^2+x)/x^2,x, algorithm="giac")

[Out]

-e^4*log(3)^2/x + log(abs(x))

________________________________________________________________________________________

maple [A]  time = 0.04, size = 15, normalized size = 0.88

method	result	size
default	\(\ln \relax (x )-\frac {{\mathrm e}^{4} \ln \relax (3)^{2}}{x}\)	\(15\)
norman	\(\ln \relax (x )-\frac {{\mathrm e}^{4} \ln \relax (3)^{2}}{x}\)	\(15\)
risch	\(\ln \relax (x )-\frac {{\mathrm e}^{4} \ln \relax (3)^{2}}{x}\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(4)*ln(3)^2+x)/x^2,x,method=_RETURNVERBOSE)

[Out]

ln(x)-exp(4)/x*ln(3)^2

________________________________________________________________________________________

maxima [A]  time = 0.35, size = 14, normalized size = 0.82 \begin {gather*} -\frac {e^{4} \log \relax (3)^{2}}{x} + \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((exp(4)*log(3)^2+x)/x^2,x, algorithm="maxima")

[Out]

-e^4*log(3)^2/x + log(x)

________________________________________________________________________________________

mupad [B]  time = 7.77, size = 14, normalized size = 0.82 \begin {gather*} \ln \relax (x)-\frac {{\mathrm {e}}^4\,{\ln \relax (3)}^2}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((x + exp(4)*log(3)^2)/x^2,x)

[Out]

log(x) - (exp(4)*log(3)^2)/x

________________________________________________________________________________________

sympy [A]  time = 0.12, size = 12, normalized size = 0.71 \begin {gather*} \log {\relax (x )} - \frac {e^{4} \log {\relax (3 )}^{2}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((exp(4)*ln(3)**2+x)/x**2,x)

[Out]

log(x) - exp(4)*log(3)**2/x

________________________________________________________________________________________