3.7.2 \(\int \frac {4335+289 x+(-289 x+5 x^2) \log (\frac {-289+5 x}{x}) \log (\log (\frac {-289+5 x}{x}))}{(-289 x+5 x^2) \log (\frac {-289+5 x}{x})} \, dx\)

Optimal. Leaf size=13 \[ (15+x) \log \left (\log \left (5-\frac {289}{x}\right )\right ) \]

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Rubi [F]  time = 0.39, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {4335+289 x+\left (-289 x+5 x^2\right ) \log \left (\frac {-289+5 x}{x}\right ) \log \left (\log \left (\frac {-289+5 x}{x}\right )\right )}{\left (-289 x+5 x^2\right ) \log \left (\frac {-289+5 x}{x}\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(4335 + 289*x + (-289*x + 5*x^2)*Log[(-289 + 5*x)/x]*Log[Log[(-289 + 5*x)/x]])/((-289*x + 5*x^2)*Log[(-289
+ 5*x)/x]),x]

[Out]

289*Defer[Int][(15 + x)/(x*(-289 + 5*x)*Log[(-289 + 5*x)/x]), x] + Defer[Int][Log[Log[5 - 289/x]], x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {4335+289 x+\left (-289 x+5 x^2\right ) \log \left (\frac {-289+5 x}{x}\right ) \log \left (\log \left (\frac {-289+5 x}{x}\right )\right )}{x (-289+5 x) \log \left (\frac {-289+5 x}{x}\right )} \, dx\\ &=\int \left (\frac {289 (15+x)}{x (-289+5 x) \log \left (5-\frac {289}{x}\right )}+\log \left (\log \left (5-\frac {289}{x}\right )\right )\right ) \, dx\\ &=289 \int \frac {15+x}{x (-289+5 x) \log \left (5-\frac {289}{x}\right )} \, dx+\int \log \left (\log \left (5-\frac {289}{x}\right )\right ) \, dx\\ &=289 \int \frac {15+x}{x (-289+5 x) \log \left (\frac {-289+5 x}{x}\right )} \, dx+\int \log \left (\log \left (5-\frac {289}{x}\right )\right ) \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 10.09, size = 23, normalized size = 1.77 \begin {gather*} 15 \log \left (\log \left (5-\frac {289}{x}\right )\right )+x \log \left (\log \left (5-\frac {289}{x}\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(4335 + 289*x + (-289*x + 5*x^2)*Log[(-289 + 5*x)/x]*Log[Log[(-289 + 5*x)/x]])/((-289*x + 5*x^2)*Log
[(-289 + 5*x)/x]),x]

[Out]

15*Log[Log[5 - 289/x]] + x*Log[Log[5 - 289/x]]

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fricas [A]  time = 0.72, size = 15, normalized size = 1.15 \begin {gather*} {\left (x + 15\right )} \log \left (\log \left (\frac {5 \, x - 289}{x}\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((5*x^2-289*x)*log((5*x-289)/x)*log(log((5*x-289)/x))+289*x+4335)/(5*x^2-289*x)/log((5*x-289)/x),x,
algorithm="fricas")

[Out]

(x + 15)*log(log((5*x - 289)/x))

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giac [B]  time = 0.47, size = 28, normalized size = 2.15 \begin {gather*} x \log \left (\log \left (\frac {5 \, x - 289}{x}\right )\right ) + 15 \, \log \left (\log \left (5 \, x - 289\right ) - \log \relax (x)\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((5*x^2-289*x)*log((5*x-289)/x)*log(log((5*x-289)/x))+289*x+4335)/(5*x^2-289*x)/log((5*x-289)/x),x,
algorithm="giac")

[Out]

x*log(log((5*x - 289)/x)) + 15*log(log(5*x - 289) - log(x))

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maple [B]  time = 0.28, size = 28, normalized size = 2.15

method	result	size
norman	\(x \ln \left (\ln \left (\frac {5 x -289}{x}\right )\right )+15 \ln \left (\ln \left (\frac {5 x -289}{x}\right )\right )\)	\(28\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((5*x^2-289*x)*ln((5*x-289)/x)*ln(ln((5*x-289)/x))+289*x+4335)/(5*x^2-289*x)/ln((5*x-289)/x),x,method=_RET
URNVERBOSE)

[Out]

x*ln(ln((5*x-289)/x))+15*ln(ln((5*x-289)/x))

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maxima [B]  time = 0.45, size = 29, normalized size = 2.23 \begin {gather*} x \log \left (\log \left (5 \, x - 289\right ) - \log \relax (x)\right ) + 15 \, \log \left (\log \left (5 \, x - 289\right ) - \log \relax (x)\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((5*x^2-289*x)*log((5*x-289)/x)*log(log((5*x-289)/x))+289*x+4335)/(5*x^2-289*x)/log((5*x-289)/x),x,
algorithm="maxima")

[Out]

x*log(log(5*x - 289) - log(x)) + 15*log(log(5*x - 289) - log(x))

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mupad [B]  time = 0.98, size = 15, normalized size = 1.15 \begin {gather*} \ln \left (\ln \left (\frac {5\,x-289}{x}\right )\right )\,\left (x+15\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(289*x - log(log((5*x - 289)/x))*log((5*x - 289)/x)*(289*x - 5*x^2) + 4335)/(log((5*x - 289)/x)*(289*x -
5*x^2)),x)

[Out]

log(log((5*x - 289)/x))*(x + 15)

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sympy [B]  time = 0.63, size = 27, normalized size = 2.08 \begin {gather*} \left (x - \frac {289}{30}\right ) \log {\left (\log {\left (\frac {5 x - 289}{x} \right )} \right )} + \frac {739 \log {\left (\log {\left (\frac {5 x - 289}{x} \right )} \right )}}{30} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((5*x**2-289*x)*ln((5*x-289)/x)*ln(ln((5*x-289)/x))+289*x+4335)/(5*x**2-289*x)/ln((5*x-289)/x),x)

[Out]

(x - 289/30)*log(log((5*x - 289)/x)) + 739*log(log((5*x - 289)/x))/30

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