3.67.6 \(\int \frac {-e^5 \log (5)+e^5 \log (5) \log (x)}{x^2} \, dx\)

Optimal. Leaf size=14 \[ 4-\frac {e^5 \log (5) \log (x)}{x} \]

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Rubi [A]  time = 0.02, antiderivative size = 12, normalized size of antiderivative = 0.86, number of steps used = 1, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {2303} \begin {gather*} -\frac {e^5 \log (5) \log (x)}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-(E^5*Log[5]) + E^5*Log[5]*Log[x])/x^2,x]

[Out]

-((E^5*Log[5]*Log[x])/x)

Rule 2303

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))*((d_.)*(x_))^(m_.), x_Symbol] :> Simp[(b*(d*x)^(m + 1)*Log[c*x^n])/(
d*(m + 1)), x] /; FreeQ[{a, b, c, d, m, n}, x] && NeQ[m, -1] && EqQ[a*(m + 1) - b*n, 0]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-\frac {e^5 \log (5) \log (x)}{x}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 12, normalized size = 0.86 \begin {gather*} -\frac {e^5 \log (5) \log (x)}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-(E^5*Log[5]) + E^5*Log[5]*Log[x])/x^2,x]

[Out]

-((E^5*Log[5]*Log[x])/x)

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fricas [A]  time = 0.61, size = 11, normalized size = 0.79 \begin {gather*} -\frac {e^{5} \log \relax (5) \log \relax (x)}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((exp(5)*log(5)*log(x)-exp(5)*log(5))/x^2,x, algorithm="fricas")

[Out]

-e^5*log(5)*log(x)/x

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giac [A]  time = 0.11, size = 11, normalized size = 0.79 \begin {gather*} -\frac {e^{5} \log \relax (5) \log \relax (x)}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((exp(5)*log(5)*log(x)-exp(5)*log(5))/x^2,x, algorithm="giac")

[Out]

-e^5*log(5)*log(x)/x

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maple [A]  time = 0.04, size = 12, normalized size = 0.86

method	result	size
norman	\(-\frac {{\mathrm e}^{5} \ln \relax (5) \ln \relax (x )}{x}\)	\(12\)
risch	\(-\frac {{\mathrm e}^{5} \ln \relax (5) \ln \relax (x )}{x}\)	\(12\)
default	\({\mathrm e}^{5} \ln \relax (5) \left (-\frac {\ln \relax (x )}{x}-\frac {1}{x}\right )+\frac {{\mathrm e}^{5} \ln \relax (5)}{x}\)	\(28\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(5)*ln(5)*ln(x)-exp(5)*ln(5))/x^2,x,method=_RETURNVERBOSE)

[Out]

-exp(5)*ln(5)*ln(x)/x

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maxima [A]  time = 0.46, size = 24, normalized size = 1.71 \begin {gather*} -\frac {{\left (e^{5} \log \relax (x) + e^{5}\right )} \log \relax (5)}{x} + \frac {e^{5} \log \relax (5)}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((exp(5)*log(5)*log(x)-exp(5)*log(5))/x^2,x, algorithm="maxima")

[Out]

-(e^5*log(x) + e^5)*log(5)/x + e^5*log(5)/x

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mupad [B]  time = 4.19, size = 11, normalized size = 0.79 \begin {gather*} -\frac {{\mathrm {e}}^5\,\ln \relax (5)\,\ln \relax (x)}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(5)*log(5) - exp(5)*log(5)*log(x))/x^2,x)

[Out]

-(exp(5)*log(5)*log(x))/x

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sympy [A]  time = 0.11, size = 12, normalized size = 0.86 \begin {gather*} - \frac {e^{5} \log {\relax (5 )} \log {\relax (x )}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((exp(5)*ln(5)*ln(x)-exp(5)*ln(5))/x**2,x)

[Out]

-exp(5)*log(5)*log(x)/x

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