3.67.57 \(\int \frac {-27+3 e^{256}-36 x^3+(27-3 e^{256}+9 x-18 x^3) \log (x)+(-27+3 e^{256}-9 x+18 x^3) \log (\frac {1}{3} (-9+e^{256}-3 x+6 x^3))}{(-9+e^{256}-3 x+6 x^3) \log ^2(x)+(18-2 e^{256}+6 x-12 x^3) \log (x) \log (\frac {1}{3} (-9+e^{256}-3 x+6 x^3))+(-9+e^{256}-3 x+6 x^3) \log ^2(\frac {1}{3} (-9+e^{256}-3 x+6 x^3))} \, dx\)

Optimal. Leaf size=28 \[ \frac {3 x}{-\log (x)+\log \left (-3+\frac {e^{256}}{3}-x+2 x^3\right )} \]

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Rubi [F]  time = 7.57, 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 {-27+3 e^{256}-36 x^3+\left (27-3 e^{256}+9 x-18 x^3\right ) \log (x)+\left (-27+3 e^{256}-9 x+18 x^3\right ) \log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )}{\left (-9+e^{256}-3 x+6 x^3\right ) \log ^2(x)+\left (18-2 e^{256}+6 x-12 x^3\right ) \log (x) \log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )+\left (-9+e^{256}-3 x+6 x^3\right ) \log ^2\left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-27 + 3*E^256 - 36*x^3 + (27 - 3*E^256 + 9*x - 18*x^3)*Log[x] + (-27 + 3*E^256 - 9*x + 18*x^3)*Log[(-9 +
E^256 - 3*x + 6*x^3)/3])/((-9 + E^256 - 3*x + 6*x^3)*Log[x]^2 + (18 - 2*E^256 + 6*x - 12*x^3)*Log[x]*Log[(-9 +
E^256 - 3*x + 6*x^3)/3] + (-9 + E^256 - 3*x + 6*x^3)*Log[(-9 + E^256 - 3*x + 6*x^3)/3]^2),x]

[Out]

-6*Defer[Int][(Log[3] + Log[x] - Log[-9 + E^256 - 3*x + 6*x^3])^(-2), x] - 9*(9 - E^256)*Defer[Int][1/((-9 + E
^256 - 3*x + 6*x^3)*(Log[3] + Log[x] - Log[-9 + E^256 - 3*x + 6*x^3])^2), x] - 18*Defer[Int][x/((-9 + E^256 -
3*x + 6*x^3)*(Log[3] + Log[x] - Log[-9 + E^256 - 3*x + 6*x^3])^2), x] - 3*Defer[Int][Log[x]/(Log[3] + Log[x] -
Log[-9 + E^256 - 3*x + 6*x^3])^2, x] + 3*Defer[Int][Log[(-9 + E^256 - 3*x + 6*x^3)/3]/(Log[3] + Log[x] - Log[
-9 + E^256 - 3*x + 6*x^3])^2, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {3 \left (9 \left (1-\frac {e^{256}}{9}\right )+12 x^3+\left (-9+e^{256}-3 x+6 x^3\right ) \log (x)-\left (-9+e^{256}-3 x+6 x^3\right ) \log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )\right )}{\left (9-e^{256}+3 x-6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx\\ &=3 \int \frac {9 \left (1-\frac {e^{256}}{9}\right )+12 x^3+\left (-9+e^{256}-3 x+6 x^3\right ) \log (x)-\left (-9+e^{256}-3 x+6 x^3\right ) \log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )}{\left (9-e^{256}+3 x-6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx\\ &=3 \int \left (\frac {-9+e^{256}}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2}-\frac {12 x^3}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2}+\frac {9 \left (1-\frac {e^{256}}{9}\right ) \log (x)}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2}+\frac {3 x \log (x)}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2}-\frac {6 x^3 \log (x)}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2}-\frac {9 \left (1-\frac {e^{256}}{9}\right ) \log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2}-\frac {3 x \log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2}+\frac {6 x^3 \log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2}\right ) \, dx\\ &=9 \int \frac {x \log (x)}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx-9 \int \frac {x \log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx-18 \int \frac {x^3 \log (x)}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx+18 \int \frac {x^3 \log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx-36 \int \frac {x^3}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx-\left (3 \left (9-e^{256}\right )\right ) \int \frac {1}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx+\left (3 \left (9-e^{256}\right )\right ) \int \frac {\log (x)}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx-\left (3 \left (9-e^{256}\right )\right ) \int \frac {\log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx\\ &=9 \int \frac {x \log (x)}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx-9 \int \frac {x \log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx-18 \int \left (\frac {\log (x)}{6 \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2}-\frac {\left (-9+e^{256}-3 x\right ) \log (x)}{6 \left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2}\right ) \, dx+18 \int \left (\frac {\log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )}{6 \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2}-\frac {\left (-9+e^{256}-3 x\right ) \log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )}{6 \left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2}\right ) \, dx-36 \int \left (\frac {1}{6 \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2}+\frac {9-e^{256}+3 x}{6 \left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2}\right ) \, dx-\left (3 \left (9-e^{256}\right )\right ) \int \frac {1}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx+\left (3 \left (9-e^{256}\right )\right ) \int \frac {\log (x)}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx-\left (3 \left (9-e^{256}\right )\right ) \int \frac {\log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx\\ &=-\left (3 \int \frac {\log (x)}{\left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx\right )+3 \int \frac {\left (-9+e^{256}-3 x\right ) \log (x)}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx+3 \int \frac {\log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )}{\left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx-3 \int \frac {\left (-9+e^{256}-3 x\right ) \log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx-6 \int \frac {1}{\left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx-6 \int \frac {9-e^{256}+3 x}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx+9 \int \frac {x \log (x)}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx-9 \int \frac {x \log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx-\left (3 \left (9-e^{256}\right )\right ) \int \frac {1}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx+\left (3 \left (9-e^{256}\right )\right ) \int \frac {\log (x)}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx-\left (3 \left (9-e^{256}\right )\right ) \int \frac {\log \left (\frac {1}{3} \left (-9+e^{256}-3 x+6 x^3\right )\right )}{\left (-9+e^{256}-3 x+6 x^3\right ) \left (\log (3)+\log (x)-\log \left (-9+e^{256}-3 x+6 x^3\right )\right )^2} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.08, size = 28, normalized size = 1.00 \begin {gather*} \frac {3 x}{-\log (3)-\log (x)+\log \left (-9+e^{256}-3 x+6 x^3\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-27 + 3*E^256 - 36*x^3 + (27 - 3*E^256 + 9*x - 18*x^3)*Log[x] + (-27 + 3*E^256 - 9*x + 18*x^3)*Log[
(-9 + E^256 - 3*x + 6*x^3)/3])/((-9 + E^256 - 3*x + 6*x^3)*Log[x]^2 + (18 - 2*E^256 + 6*x - 12*x^3)*Log[x]*Log
[(-9 + E^256 - 3*x + 6*x^3)/3] + (-9 + E^256 - 3*x + 6*x^3)*Log[(-9 + E^256 - 3*x + 6*x^3)/3]^2),x]

[Out]

(3*x)/(-Log[3] - Log[x] + Log[-9 + E^256 - 3*x + 6*x^3])

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fricas [A]  time = 0.53, size = 25, normalized size = 0.89 \begin {gather*} \frac {3 \, x}{\log \left (2 \, x^{3} - x + \frac {1}{3} \, e^{256} - 3\right ) - \log \relax (x)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((3*exp(256)+18*x^3-9*x-27)*log(1/3*exp(256)+2*x^3-x-3)+(-3*exp(256)-18*x^3+9*x+27)*log(x)+3*exp(256
)-36*x^3-27)/((exp(256)+6*x^3-3*x-9)*log(1/3*exp(256)+2*x^3-x-3)^2+(-2*exp(256)-12*x^3+6*x+18)*log(x)*log(1/3*
exp(256)+2*x^3-x-3)+(exp(256)+6*x^3-3*x-9)*log(x)^2),x, algorithm="fricas")

[Out]

3*x/(log(2*x^3 - x + 1/3*e^256 - 3) - log(x))

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giac [F(-2)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: TypeError} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((3*exp(256)+18*x^3-9*x-27)*log(1/3*exp(256)+2*x^3-x-3)+(-3*exp(256)-18*x^3+9*x+27)*log(x)+3*exp(256
)-36*x^3-27)/((exp(256)+6*x^3-3*x-9)*log(1/3*exp(256)+2*x^3-x-3)^2+(-2*exp(256)-12*x^3+6*x+18)*log(x)*log(1/3*
exp(256)+2*x^3-x-3)+(exp(256)+6*x^3-3*x-9)*log(x)^2),x, algorithm="giac")

[Out]

Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,sageVARx):;OUTP
UT:Francis algorithm not precise enough for[-3.70075001019e+224,0.0,-9.0,1.0]Francis algorithm failure for[-1.
0,0.0,1.231

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maple [A]  time = 0.04, size = 26, normalized size = 0.93

method	result	size
risch	\(-\frac {3 x}{\ln \relax (x )-\ln \left (\frac {{\mathrm e}^{256}}{3}+2 x^{3}-x -3\right )}\)	\(26\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((3*exp(256)+18*x^3-9*x-27)*ln(1/3*exp(256)+2*x^3-x-3)+(-3*exp(256)-18*x^3+9*x+27)*ln(x)+3*exp(256)-36*x^3
-27)/((exp(256)+6*x^3-3*x-9)*ln(1/3*exp(256)+2*x^3-x-3)^2+(-2*exp(256)-12*x^3+6*x+18)*ln(x)*ln(1/3*exp(256)+2*
x^3-x-3)+(exp(256)+6*x^3-3*x-9)*ln(x)^2),x,method=_RETURNVERBOSE)

[Out]

-3*x/(ln(x)-ln(1/3*exp(256)+2*x^3-x-3))

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maxima [A]  time = 0.51, size = 25, normalized size = 0.89 \begin {gather*} -\frac {3 \, x}{\log \relax (3) - \log \left (6 \, x^{3} - 3 \, x + e^{256} - 9\right ) + \log \relax (x)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((3*exp(256)+18*x^3-9*x-27)*log(1/3*exp(256)+2*x^3-x-3)+(-3*exp(256)-18*x^3+9*x+27)*log(x)+3*exp(256
)-36*x^3-27)/((exp(256)+6*x^3-3*x-9)*log(1/3*exp(256)+2*x^3-x-3)^2+(-2*exp(256)-12*x^3+6*x+18)*log(x)*log(1/3*
exp(256)+2*x^3-x-3)+(exp(256)+6*x^3-3*x-9)*log(x)^2),x, algorithm="maxima")

[Out]

-3*x/(log(3) - log(6*x^3 - 3*x + e^256 - 9) + log(x))

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mupad [B]  time = 4.71, size = 25, normalized size = 0.89 \begin {gather*} \frac {3\,x}{\ln \left (2\,x^3-x+\frac {{\mathrm {e}}^{256}}{3}-3\right )-\ln \relax (x)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(exp(256)/3 - x + 2*x^3 - 3)*(9*x - 3*exp(256) - 18*x^3 + 27) - 3*exp(256) - log(x)*(9*x - 3*exp(256)
- 18*x^3 + 27) + 36*x^3 + 27)/(log(exp(256)/3 - x + 2*x^3 - 3)^2*(3*x - exp(256) - 6*x^3 + 9) + log(x)^2*(3*x
- exp(256) - 6*x^3 + 9) - log(exp(256)/3 - x + 2*x^3 - 3)*log(x)*(6*x - 2*exp(256) - 12*x^3 + 18)),x)

[Out]

(3*x)/(log(exp(256)/3 - x + 2*x^3 - 3) - log(x))

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sympy [A]  time = 0.38, size = 20, normalized size = 0.71 \begin {gather*} \frac {3 x}{- \log {\relax (x )} + \log {\left (2 x^{3} - x - 3 + \frac {e^{256}}{3} \right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((3*exp(256)+18*x**3-9*x-27)*ln(1/3*exp(256)+2*x**3-x-3)+(-3*exp(256)-18*x**3+9*x+27)*ln(x)+3*exp(25
6)-36*x**3-27)/((exp(256)+6*x**3-3*x-9)*ln(1/3*exp(256)+2*x**3-x-3)**2+(-2*exp(256)-12*x**3+6*x+18)*ln(x)*ln(1
/3*exp(256)+2*x**3-x-3)+(exp(256)+6*x**3-3*x-9)*ln(x)**2),x)

[Out]

3*x/(-log(x) + log(2*x**3 - x - 3 + exp(256)/3))

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