∫ (128x−18x3+36x4−18x5+(−768−256x+324x2−756x3+252x4+180x5) log(3+x)) log( 4096 log(3+x)_________________________________ 4096x2−1152x4+2304x5−1071x6−324x7+486x8−324x9+81x10 ) ____________________________________________________________________________________________________________________________________________________________________________________________(−192x−64x2 +27x3 −45x4 +9x5 +9x6 ) log (3+x) dx

3.40.46 \(\int \frac {(128 x-18 x^3+36 x^4-18 x^5+(-768-256 x+324 x^2-756 x^3+252 x^4+180 x^5) \log (3+x)) \log (\frac {4096 \log (3+x)}{4096 x^2-1152 x^4+2304 x^5-1071 x^6-324 x^7+486 x^8-324 x^9+81 x^{10}})}{(-192 x-64 x^2+27 x^3-45 x^4+9 x^5+9 x^6) \log (3+x)} \, dx\)

Optimal. Leaf size=30 \[ 4-\log ^2\left (\frac {\log (3+x)}{\left (x-\frac {9}{64} x \left (-x+x^2\right )^2\right )^2}\right ) \]

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Rubi [F] time = 151.82, 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 {\left (128 x-18 x^3+36 x^4-18 x^5+\left (-768-256 x+324 x^2-756 x^3+252 x^4+180 x^5\right ) \log (3+x)\right ) \log \left (\frac {4096 \log (3+x)}{4096 x^2-1152 x^4+2304 x^5-1071 x^6-324 x^7+486 x^8-324 x^9+81 x^{10}}\right )}{\left (-192 x-64 x^2+27 x^3-45 x^4+9 x^5+9 x^6\right ) \log (3+x)} \, dx \end {gather*}

Veriﬁcation is not applicable to the result.

[In]

Int[((128*x - 18*x^3 + 36*x^4 - 18*x^5 + (-768 - 256*x + 324*x^2 - 756*x^3 + 252*x^4 + 180*x^5)*Log[3 + x])*Lo

g[(4096*Log[3 + x])/(4096*x^2 - 1152*x^4 + 2304*x^5 - 1071*x^6 - 324*x^7 + 486*x^8 - 324*x^9 + 81*x^10)])/((-1

92*x - 64*x^2 + 27*x^3 - 45*x^4 + 9*x^5 + 9*x^6)*Log[3 + x]),x]

[Out]

(-7555*Sqrt[5/21]*ArcTanh[Sqrt[3/35]*(1 - 2*x)])/64 + (297*Sqrt[15/7]*ArcTanh[Sqrt[3/35]*(1 - 2*x)])/8 - (1921

*Sqrt[35/3]*ArcTanh[Sqrt[3/35]*(1 - 2*x)])/704 + (27*Sqrt[105]*ArcTanh[Sqrt[3/35]*(1 - 2*x)])/22 - (24*I)*Sqrt

[3/29]*Defer[Int][Log[(4096*Log[3 + x])/(x^2*(64 - 9*x^2 + 18*x^3 - 9*x^4)^2)]/(3 + I*Sqrt[87] - 6*x), x] - (3

63*Sqrt[3/35]*Defer[Int][Log[(4096*Log[3 + x])/(x^2*(64 - 9*x^2 + 18*x^3 - 9*x^4)^2)]/(3 + Sqrt[105] - 6*x), x

])/14 - (507*Sqrt[15/7]*Defer[Int][Log[(4096*Log[3 + x])/(x^2*(64 - 9*x^2 + 18*x^3 - 9*x^4)^2)]/(3 + Sqrt[105]

- 6*x), x])/14 + 33*Sqrt[21/5]*Defer[Int][Log[(4096*Log[3 + x])/(x^2*(64 - 9*x^2 + 18*x^3 - 9*x^4)^2)]/(3 + S

qrt[105] - 6*x), x] + 4*Defer[Int][Log[(4096*Log[3 + x])/(x^2*(64 - 9*x^2 + 18*x^3 - 9*x^4)^2)]/x, x] + (24*(2

9 - I*Sqrt[87])*Defer[Int][Log[(4096*Log[3 + x])/(x^2*(64 - 9*x^2 + 18*x^3 - 9*x^4)^2)]/(-3 - I*Sqrt[87] + 6*x

), x])/29 - (24*I)*Sqrt[3/29]*Defer[Int][Log[(4096*Log[3 + x])/(x^2*(64 - 9*x^2 + 18*x^3 - 9*x^4)^2)]/(-3 + I*

Sqrt[87] + 6*x), x] + (24*(29 + I*Sqrt[87])*Defer[Int][Log[(4096*Log[3 + x])/(x^2*(64 - 9*x^2 + 18*x^3 - 9*x^4

)^2)]/(-3 + I*Sqrt[87] + 6*x), x])/29 + (24*(35 + Sqrt[105])*Defer[Int][Log[(4096*Log[3 + x])/(x^2*(64 - 9*x^2

+ 18*x^3 - 9*x^4)^2)]/(-3 - Sqrt[105] + 6*x), x])/35 - (363*Sqrt[3/35]*Defer[Int][Log[(4096*Log[3 + x])/(x^2*

(64 - 9*x^2 + 18*x^3 - 9*x^4)^2)]/(-3 + Sqrt[105] + 6*x), x])/14 - (507*Sqrt[15/7]*Defer[Int][Log[(4096*Log[3

+ x])/(x^2*(64 - 9*x^2 + 18*x^3 - 9*x^4)^2)]/(-3 + Sqrt[105] + 6*x), x])/14 + 33*Sqrt[21/5]*Defer[Int][Log[(40

96*Log[3 + x])/(x^2*(64 - 9*x^2 + 18*x^3 - 9*x^4)^2)]/(-3 + Sqrt[105] + 6*x), x] + (24*(35 - Sqrt[105])*Defer[

Int][Log[(4096*Log[3 + x])/(x^2*(64 - 9*x^2 + 18*x^3 - 9*x^4)^2)]/(-3 + Sqrt[105] + 6*x), x])/35 - 2*Defer[Int

][Log[(4096*Log[3 + x])/(x^2*(64 - 9*x^2 + 18*x^3 - 9*x^4)^2)]/((3 + x)*Log[3 + x]), x]

Rubi steps

Aborted

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Mathematica [A] time = 0.07, size = 33, normalized size = 1.10 \begin {gather*} -\log ^2\left (\frac {4096 \log (3+x)}{x^2 \left (64-9 x^2+18 x^3-9 x^4\right )^2}\right ) \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

Integrate[((128*x - 18*x^3 + 36*x^4 - 18*x^5 + (-768 - 256*x + 324*x^2 - 756*x^3 + 252*x^4 + 180*x^5)*Log[3 +

x])*Log[(4096*Log[3 + x])/(4096*x^2 - 1152*x^4 + 2304*x^5 - 1071*x^6 - 324*x^7 + 486*x^8 - 324*x^9 + 81*x^10)]

)/((-192*x - 64*x^2 + 27*x^3 - 45*x^4 + 9*x^5 + 9*x^6)*Log[3 + x]),x]

[Out]

-Log[(4096*Log[3 + x])/(x^2*(64 - 9*x^2 + 18*x^3 - 9*x^4)^2)]^2

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fricas [A] time = 0.86, size = 54, normalized size = 1.80 \begin {gather*} -\log \left (\frac {4096 \, \log \left (x + 3\right )}{81 \, x^{10} - 324 \, x^{9} + 486 \, x^{8} - 324 \, x^{7} - 1071 \, x^{6} + 2304 \, x^{5} - 1152 \, x^{4} + 4096 \, x^{2}}\right )^{2} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((180*x^5+252*x^4-756*x^3+324*x^2-256*x-768)*log(3+x)-18*x^5+36*x^4-18*x^3+128*x)*log(4096*log(3+x)/

(81*x^10-324*x^9+486*x^8-324*x^7-1071*x^6+2304*x^5-1152*x^4+4096*x^2))/(9*x^6+9*x^5-45*x^4+27*x^3-64*x^2-192*x

)/log(3+x),x, algorithm="fricas")

[Out]

-log(4096*log(x + 3)/(81*x^10 - 324*x^9 + 486*x^8 - 324*x^7 - 1071*x^6 + 2304*x^5 - 1152*x^4 + 4096*x^2))^2

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giac [B] time = 0.50, size = 207, normalized size = 6.90 \begin {gather*} -2 \, {\left (2 \, \log \left (9 \, x^{4} - 18 \, x^{3} + 9 \, x^{2} - 64\right ) + 2 \, \log \relax (x) - \log \left (\log \left (x + 3\right )\right )\right )} \log \left (81 \, x^{10} - 324 \, x^{9} + 486 \, x^{8} - 324 \, x^{7} - 1071 \, x^{6} + 2304 \, x^{5} - 1152 \, x^{4} + 4096 \, x^{2}\right ) + 4 \, {\left (2 \, \log \left (9 \, x^{4} - 18 \, x^{3} + 9 \, x^{2} - 64\right ) + 2 \, \log \relax (x) - \log \left (\log \left (x + 3\right )\right )\right )} \log \left (9 \, x^{4} - 18 \, x^{3} + 9 \, x^{2} - 64\right ) - 4 \, \log \left (9 \, x^{4} - 18 \, x^{3} + 9 \, x^{2} - 64\right )^{2} + 4 \, \log \relax (x)^{2} + 4 \, {\left (\log \left (9 \, x^{4} - 18 \, x^{3} + 9 \, x^{2} - 64\right ) + \log \relax (x)\right )} \log \left (4096 \, \log \left (x + 3\right )\right ) - \log \left (4096 \, \log \left (x + 3\right )\right )^{2} - 4 \, \log \relax (x) \log \left (\log \left (x + 3\right )\right ) \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((180*x^5+252*x^4-756*x^3+324*x^2-256*x-768)*log(3+x)-18*x^5+36*x^4-18*x^3+128*x)*log(4096*log(3+x)/

(81*x^10-324*x^9+486*x^8-324*x^7-1071*x^6+2304*x^5-1152*x^4+4096*x^2))/(9*x^6+9*x^5-45*x^4+27*x^3-64*x^2-192*x

)/log(3+x),x, algorithm="giac")

[Out]

-2*(2*log(9*x^4 - 18*x^3 + 9*x^2 - 64) + 2*log(x) - log(log(x + 3)))*log(81*x^10 - 324*x^9 + 486*x^8 - 324*x^7

- 1071*x^6 + 2304*x^5 - 1152*x^4 + 4096*x^2) + 4*(2*log(9*x^4 - 18*x^3 + 9*x^2 - 64) + 2*log(x) - log(log(x +

3)))*log(9*x^4 - 18*x^3 + 9*x^2 - 64) - 4*log(9*x^4 - 18*x^3 + 9*x^2 - 64)^2 + 4*log(x)^2 + 4*(log(9*x^4 - 18

*x^3 + 9*x^2 - 64) + log(x))*log(4096*log(x + 3)) - log(4096*log(x + 3))^2 - 4*log(x)*log(log(x + 3))

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maple [F] time = 0.01, size = 0, normalized size = 0.00 \[\int \frac {\left (\left (180 x^{5}+252 x^{4}-756 x^{3}+324 x^{2}-256 x -768\right ) \ln \left (3+x \right )-18 x^{5}+36 x^{4}-18 x^{3}+128 x \right ) \ln \left (\frac {4096 \ln \left (3+x \right )}{81 x^{10}-324 x^{9}+486 x^{8}-324 x^{7}-1071 x^{6}+2304 x^{5}-1152 x^{4}+4096 x^{2}}\right )}{\left (9 x^{6}+9 x^{5}-45 x^{4}+27 x^{3}-64 x^{2}-192 x \right ) \ln \left (3+x \right )}\, dx\]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(((180*x^5+252*x^4-756*x^3+324*x^2-256*x-768)*ln(3+x)-18*x^5+36*x^4-18*x^3+128*x)*ln(4096*ln(3+x)/(81*x^10-

324*x^9+486*x^8-324*x^7-1071*x^6+2304*x^5-1152*x^4+4096*x^2))/(9*x^6+9*x^5-45*x^4+27*x^3-64*x^2-192*x)/ln(3+x)

,x)

[Out]

int(((180*x^5+252*x^4-756*x^3+324*x^2-256*x-768)*ln(3+x)-18*x^5+36*x^4-18*x^3+128*x)*ln(4096*ln(3+x)/(81*x^10-

324*x^9+486*x^8-324*x^7-1071*x^6+2304*x^5-1152*x^4+4096*x^2))/(9*x^6+9*x^5-45*x^4+27*x^3-64*x^2-192*x)/ln(3+x)

,x)

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maxima [B] time = 0.43, size = 206, normalized size = 6.87 \begin {gather*} 4 \, {\left (2 \, \log \left (3 \, x^{2} - 3 \, x - 8\right ) + 2 \, \log \relax (x) - \log \left (\log \left (x + 3\right )\right )\right )} \log \left (3 \, x^{2} - 3 \, x + 8\right ) + 4 \, \log \left (3 \, x^{2} - 3 \, x + 8\right )^{2} + 4 \, {\left (2 \, \log \relax (x) - \log \left (\log \left (x + 3\right )\right )\right )} \log \left (3 \, x^{2} - 3 \, x - 8\right ) + 4 \, \log \left (3 \, x^{2} - 3 \, x - 8\right )^{2} + 4 \, \log \relax (x)^{2} + 2 \, {\left (2 \, \log \left (3 \, x^{2} - 3 \, x + 8\right ) + 2 \, \log \left (3 \, x^{2} - 3 \, x - 8\right ) + 2 \, \log \relax (x) - \log \left (\log \left (x + 3\right )\right )\right )} \log \left (\frac {4096 \, \log \left (x + 3\right )}{81 \, x^{10} - 324 \, x^{9} + 486 \, x^{8} - 324 \, x^{7} - 1071 \, x^{6} + 2304 \, x^{5} - 1152 \, x^{4} + 4096 \, x^{2}}\right ) - 4 \, \log \relax (x) \log \left (\log \left (x + 3\right )\right ) + \log \left (\log \left (x + 3\right )\right )^{2} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((180*x^5+252*x^4-756*x^3+324*x^2-256*x-768)*log(3+x)-18*x^5+36*x^4-18*x^3+128*x)*log(4096*log(3+x)/

(81*x^10-324*x^9+486*x^8-324*x^7-1071*x^6+2304*x^5-1152*x^4+4096*x^2))/(9*x^6+9*x^5-45*x^4+27*x^3-64*x^2-192*x

)/log(3+x),x, algorithm="maxima")

[Out]

4*(2*log(3*x^2 - 3*x - 8) + 2*log(x) - log(log(x + 3)))*log(3*x^2 - 3*x + 8) + 4*log(3*x^2 - 3*x + 8)^2 + 4*(2

*log(x) - log(log(x + 3)))*log(3*x^2 - 3*x - 8) + 4*log(3*x^2 - 3*x - 8)^2 + 4*log(x)^2 + 2*(2*log(3*x^2 - 3*x

+ 8) + 2*log(3*x^2 - 3*x - 8) + 2*log(x) - log(log(x + 3)))*log(4096*log(x + 3)/(81*x^10 - 324*x^9 + 486*x^8

- 324*x^7 - 1071*x^6 + 2304*x^5 - 1152*x^4 + 4096*x^2)) - 4*log(x)*log(log(x + 3)) + log(log(x + 3))^2

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mupad [B] time = 2.69, size = 54, normalized size = 1.80 \begin {gather*} -{\ln \left (\frac {4096\,\ln \left (x+3\right )}{81\,x^{10}-324\,x^9+486\,x^8-324\,x^7-1071\,x^6+2304\,x^5-1152\,x^4+4096\,x^2}\right )}^2 \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int((log((4096*log(x + 3))/(4096*x^2 - 1152*x^4 + 2304*x^5 - 1071*x^6 - 324*x^7 + 486*x^8 - 324*x^9 + 81*x^10)

)*(log(x + 3)*(256*x - 324*x^2 + 756*x^3 - 252*x^4 - 180*x^5 + 768) - 128*x + 18*x^3 - 36*x^4 + 18*x^5))/(log(

x + 3)*(192*x + 64*x^2 - 27*x^3 + 45*x^4 - 9*x^5 - 9*x^6)),x)

[Out]

-log((4096*log(x + 3))/(4096*x^2 - 1152*x^4 + 2304*x^5 - 1071*x^6 - 324*x^7 + 486*x^8 - 324*x^9 + 81*x^10))^2

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sympy [A] time = 0.70, size = 51, normalized size = 1.70 \begin {gather*} - \log {\left (\frac {4096 \log {\left (x + 3 \right )}}{81 x^{10} - 324 x^{9} + 486 x^{8} - 324 x^{7} - 1071 x^{6} + 2304 x^{5} - 1152 x^{4} + 4096 x^{2}} \right )}^{2} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((180*x**5+252*x**4-756*x**3+324*x**2-256*x-768)*ln(3+x)-18*x**5+36*x**4-18*x**3+128*x)*ln(4096*ln(3

+x)/(81*x**10-324*x**9+486*x**8-324*x**7-1071*x**6+2304*x**5-1152*x**4+4096*x**2))/(9*x**6+9*x**5-45*x**4+27*x

**3-64*x**2-192*x)/ln(3+x),x)

[Out]

-log(4096*log(x + 3)/(81*x**10 - 324*x**9 + 486*x**8 - 324*x**7 - 1071*x**6 + 2304*x**5 - 1152*x**4 + 4096*x**

2))**2

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