3.85.44 \(\int \frac {-8+36 e^5 x^5 \log (5)}{-4-4 x+3 e^5 x^6 \log (5)} \, dx\)

Optimal. Leaf size=20 \[ \log \left (\left (-2-2 x+\frac {3}{2} e^5 x^6 \log (5)\right )^2\right ) \]

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Rubi [A]  time = 0.02, antiderivative size = 18, normalized size of antiderivative = 0.90, number of steps used = 1, number of rules used = 1, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.033, Rules used = {1587} \begin {gather*} 2 \log \left (-3 e^5 x^6 \log (5)+4 x+4\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-8 + 36*E^5*x^5*Log[5])/(-4 - 4*x + 3*E^5*x^6*Log[5]),x]

[Out]

2*Log[4 + 4*x - 3*E^5*x^6*Log[5]]

Rule 1587

Int[(Pp_)/(Qq_), x_Symbol] :> With[{p = Expon[Pp, x], q = Expon[Qq, x]}, Simp[(Coeff[Pp, x, p]*Log[RemoveConte
nt[Qq, x]])/(q*Coeff[Qq, x, q]), x] /; EqQ[p, q - 1] && EqQ[Pp, Simplify[(Coeff[Pp, x, p]*D[Qq, x])/(q*Coeff[Q
q, x, q])]]] /; PolyQ[Pp, x] && PolyQ[Qq, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=2 \log \left (4+4 x-3 e^5 x^6 \log (5)\right )\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.01, size = 18, normalized size = 0.90 \begin {gather*} 2 \log \left (4+4 x-3 e^5 x^6 \log (5)\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-8 + 36*E^5*x^5*Log[5])/(-4 - 4*x + 3*E^5*x^6*Log[5]),x]

[Out]

2*Log[4 + 4*x - 3*E^5*x^6*Log[5]]

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fricas [A]  time = 0.67, size = 17, normalized size = 0.85 \begin {gather*} 2 \, \log \left (3 \, x^{6} e^{5} \log \relax (5) - 4 \, x - 4\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((36*x^5*exp(5)*log(5)-8)/(3*x^6*exp(5)*log(5)-4*x-4),x, algorithm="fricas")

[Out]

2*log(3*x^6*e^5*log(5) - 4*x - 4)

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giac [A]  time = 0.14, size = 18, normalized size = 0.90 \begin {gather*} 2 \, \log \left ({\left | 3 \, x^{6} e^{5} \log \relax (5) - 4 \, x - 4 \right |}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((36*x^5*exp(5)*log(5)-8)/(3*x^6*exp(5)*log(5)-4*x-4),x, algorithm="giac")

[Out]

2*log(abs(3*x^6*e^5*log(5) - 4*x - 4))

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maple [A]  time = 0.05, size = 18, normalized size = 0.90

method	result	size
default	\(2 \ln \left (3 x^{6} {\mathrm e}^{5} \ln \relax (5)-4 x -4\right )\)	\(18\)
norman	\(2 \ln \left (3 x^{6} {\mathrm e}^{5} \ln \relax (5)-4 x -4\right )\)	\(18\)
risch	\(2 \ln \left (3 x^{6} {\mathrm e}^{5} \ln \relax (5)-4 x -4\right )\)	\(18\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((36*x^5*exp(5)*ln(5)-8)/(3*x^6*exp(5)*ln(5)-4*x-4),x,method=_RETURNVERBOSE)

[Out]

2*ln(3*x^6*exp(5)*ln(5)-4*x-4)

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maxima [A]  time = 0.41, size = 17, normalized size = 0.85 \begin {gather*} 2 \, \log \left (3 \, x^{6} e^{5} \log \relax (5) - 4 \, x - 4\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((36*x^5*exp(5)*log(5)-8)/(3*x^6*exp(5)*log(5)-4*x-4),x, algorithm="maxima")

[Out]

2*log(3*x^6*e^5*log(5) - 4*x - 4)

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mupad [B]  time = 0.15, size = 17, normalized size = 0.85 \begin {gather*} 2\,\ln \left (3\,{\mathrm {e}}^5\,\ln \relax (5)\,x^6-4\,x-4\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(36*x^5*exp(5)*log(5) - 8)/(4*x - 3*x^6*exp(5)*log(5) + 4),x)

[Out]

2*log(3*x^6*exp(5)*log(5) - 4*x - 4)

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sympy [A]  time = 0.36, size = 19, normalized size = 0.95 \begin {gather*} 2 \log {\left (3 x^{6} e^{5} \log {\relax (5 )} - 4 x - 4 \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((36*x**5*exp(5)*ln(5)-8)/(3*x**6*exp(5)*ln(5)-4*x-4),x)

[Out]

2*log(3*x**6*exp(5)*log(5) - 4*x - 4)

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