3.38.35 \(\int \frac {243-81 x}{-4 x-81 x^2+81 x \log (2 e^{-e^{10}} x^3)} \, dx\)

Optimal. Leaf size=21 \[ \log \left (\frac {4}{81}+x-\log \left (2 e^{-e^{10}} x^3\right )\right ) \]

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Rubi [F]  time = 0.17, 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 {243-81 x}{-4 x-81 x^2+81 x \log \left (2 e^{-e^{10}} x^3\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(243 - 81*x)/(-4*x - 81*x^2 + 81*x*Log[(2*x^3)/E^E^10]),x]

[Out]

81*Defer[Int][(4*(1 + (81*E^10)/4) + 81*x - 81*Log[2*x^3])^(-1), x] + 243*Defer[Int][1/(x*(-4*(1 + (81*E^10)/4
) - 81*x + 81*Log[2*x^3])), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {81}{4 \left (1+\frac {81 e^{10}}{4}\right )+81 x-81 \log \left (2 x^3\right )}+\frac {243}{x \left (-4 \left (1+\frac {81 e^{10}}{4}\right )-81 x+81 \log \left (2 x^3\right )\right )}\right ) \, dx\\ &=81 \int \frac {1}{4 \left (1+\frac {81 e^{10}}{4}\right )+81 x-81 \log \left (2 x^3\right )} \, dx+243 \int \frac {1}{x \left (-4 \left (1+\frac {81 e^{10}}{4}\right )-81 x+81 \log \left (2 x^3\right )\right )} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.19, size = 19, normalized size = 0.90 \begin {gather*} \log \left (4+81 e^{10}+81 x-81 \log \left (2 x^3\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(243 - 81*x)/(-4*x - 81*x^2 + 81*x*Log[(2*x^3)/E^E^10]),x]

[Out]

Log[4 + 81*E^10 + 81*x - 81*Log[2*x^3]]

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fricas [A]  time = 0.56, size = 19, normalized size = 0.90 \begin {gather*} \log \left (-81 \, x + 81 \, \log \left (2 \, x^{3} e^{\left (-e^{10}\right )}\right ) - 4\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-81*x+243)/(81*x*log(2*x^3/exp(exp(5)^2))-81*x^2-4*x),x, algorithm="fricas")

[Out]

log(-81*x + 81*log(2*x^3*e^(-e^10)) - 4)

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giac [A]  time = 0.43, size = 18, normalized size = 0.86 \begin {gather*} \log \left (-81 \, x - 81 \, e^{10} + 81 \, \log \left (2 \, x^{3}\right ) - 4\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-81*x+243)/(81*x*log(2*x^3/exp(exp(5)^2))-81*x^2-4*x),x, algorithm="giac")

[Out]

log(-81*x - 81*e^10 + 81*log(2*x^3) - 4)

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maple [A]  time = 0.03, size = 18, normalized size = 0.86

method	result	size
risch	\(\ln \left (-x +\ln \left (2 x^{3} {\mathrm e}^{-{\mathrm e}^{10}}\right )-\frac {4}{81}\right )\)	\(18\)
norman	\(\ln \left (81 x -81 \ln \left (2 x^{3} {\mathrm e}^{-{\mathrm e}^{10}}\right )+4\right )\)	\(22\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-81*x+243)/(81*x*ln(2*x^3/exp(exp(5)^2))-81*x^2-4*x),x,method=_RETURNVERBOSE)

[Out]

ln(-x+ln(2*x^3*exp(-exp(10)))-4/81)

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maxima [A]  time = 0.60, size = 16, normalized size = 0.76 \begin {gather*} \log \left (-\frac {1}{3} \, x - \frac {1}{3} \, e^{10} + \frac {1}{3} \, \log \relax (2) + \log \relax (x) - \frac {4}{243}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-81*x+243)/(81*x*log(2*x^3/exp(exp(5)^2))-81*x^2-4*x),x, algorithm="maxima")

[Out]

log(-1/3*x - 1/3*e^10 + 1/3*log(2) + log(x) - 4/243)

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mupad [B]  time = 2.62, size = 14, normalized size = 0.67 \begin {gather*} \ln \left (x+{\mathrm {e}}^{10}-\ln \left (2\,x^3\right )+\frac {4}{81}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((81*x - 243)/(4*x - 81*x*log(2*x^3*exp(-exp(10))) + 81*x^2),x)

[Out]

log(x + exp(10) - log(2*x^3) + 4/81)

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sympy [A]  time = 0.14, size = 17, normalized size = 0.81 \begin {gather*} \log {\left (- x + \log {\left (\frac {2 x^{3}}{e^{e^{10}}} \right )} - \frac {4}{81} \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-81*x+243)/(81*x*ln(2*x**3/exp(exp(5)**2))-81*x**2-4*x),x)

[Out]

log(-x + log(2*x**3*exp(-exp(10))) - 4/81)

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