3.90.94 \(\int \frac {x+e^4 \log ^2(3)}{x^2} \, dx\) [8994]

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

[Out]

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

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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 = {45} \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 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 {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*}

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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]

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Maple [A]
time = 0.42, size = 15, normalized size = 0.88

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Maxima [A]
time = 0.26, size = 14, normalized size = 0.82 \begin {gather*} -\frac {e^{4} \log \left (3\right )^{2}}{x} + \log \left (x\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="maxima")

[Out]

-e^4*log(3)^2/x + log(x)

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Fricas [A]
time = 0.46, size = 18, normalized size = 1.06 \begin {gather*} -\frac {e^{4} \log \left (3\right )^{2} - x \log \left (x\right )}{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

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Sympy [A]
time = 0.03, size = 12, normalized size = 0.71 \begin {gather*} \log {\left (x \right )} - \frac {e^{4} \log {\left (3 \right )}^{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

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Giac [A]
time = 0.40, size = 15, normalized size = 0.88 \begin {gather*} -\frac {e^{4} \log \left (3\right )^{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))

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

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