3.31.94 \(\int \frac {288-96 x-568 x^2+208 x^3+304 x^4-96 x^5-24 x^6+(-72 x+24 x^2+142 x^3-52 x^4-76 x^5+24 x^6+6 x^7) \log (\frac {9-3 x-8 x^2+3 x^3}{-3+3 x^2})}{-9 x^3+3 x^4+17 x^5-6 x^6-8 x^7+3 x^8} \, dx\)

Optimal. Leaf size=28 \[ \left (\frac {4}{x}-\log \left (-3+x-\frac {x}{3 \left (\frac {1}{x}-x\right )}\right )\right )^2 \]

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Rubi [F]  time = 27.00, 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 {288-96 x-568 x^2+208 x^3+304 x^4-96 x^5-24 x^6+\left (-72 x+24 x^2+142 x^3-52 x^4-76 x^5+24 x^6+6 x^7\right ) \log \left (\frac {9-3 x-8 x^2+3 x^3}{-3+3 x^2}\right )}{-9 x^3+3 x^4+17 x^5-6 x^6-8 x^7+3 x^8} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(288 - 96*x - 568*x^2 + 208*x^3 + 304*x^4 - 96*x^5 - 24*x^6 + (-72*x + 24*x^2 + 142*x^3 - 52*x^4 - 76*x^5
+ 24*x^6 + 6*x^7)*Log[(9 - 3*x - 8*x^2 + 3*x^3)/(-3 + 3*x^2)])/(-9*x^3 + 3*x^4 + 17*x^5 - 6*x^6 - 8*x^7 + 3*x^
8),x]

[Out]

16/x^2 - Log[-1 + x]^2 - 2*Log[-1 + x]*Log[(1 + x)/2] - 2*Log[(1 - x)/2]*Log[1 + x] - Log[1 + x]^2 - (8*Log[-1
/3*(9 - 3*x - 8*x^2 + 3*x^3)/(1 - x^2)])/x - 2*Log[-1 + x]*Log[-1/3*(9 - 3*x - 8*x^2 + 3*x^3)/(1 - x^2)] - 2*L
og[1 + x]*Log[-1/3*(9 - 3*x - 8*x^2 + 3*x^3)/(1 - x^2)] - 2*PolyLog[2, (1 - x)/2] - 2*PolyLog[2, (1 + x)/2] -
6*Defer[Int][Log[-1 + x]/(9 - 3*x - 8*x^2 + 3*x^3), x] - 32*Defer[Int][(x*Log[-1 + x])/(9 - 3*x - 8*x^2 + 3*x^
3), x] + 18*Defer[Int][(x^2*Log[-1 + x])/(9 - 3*x - 8*x^2 + 3*x^3), x] - 6*Defer[Int][Log[1 + x]/(9 - 3*x - 8*
x^2 + 3*x^3), x] - 32*Defer[Int][(x*Log[1 + x])/(9 - 3*x - 8*x^2 + 3*x^3), x] + 18*Defer[Int][(x^2*Log[1 + x])
/(9 - 3*x - 8*x^2 + 3*x^3), x] - 6*Defer[Int][Log[(9 - 3*x - 8*x^2 + 3*x^3)/(-3 + 3*x^2)]/(9 - 3*x - 8*x^2 + 3
*x^3), x] - 32*Defer[Int][(x*Log[(9 - 3*x - 8*x^2 + 3*x^3)/(-3 + 3*x^2)])/(9 - 3*x - 8*x^2 + 3*x^3), x] + 18*D
efer[Int][(x^2*Log[(9 - 3*x - 8*x^2 + 3*x^3)/(-3 + 3*x^2)])/(9 - 3*x - 8*x^2 + 3*x^3), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 \left (36-12 x-71 x^2+26 x^3+38 x^4-12 x^5-3 x^6\right ) \left (-4+x \log \left (\frac {9-3 x-8 x^2+3 x^3}{-3+3 x^2}\right )\right )}{x^3 \left (9-3 x-17 x^2+6 x^3+8 x^4-3 x^5\right )} \, dx\\ &=2 \int \frac {\left (36-12 x-71 x^2+26 x^3+38 x^4-12 x^5-3 x^6\right ) \left (-4+x \log \left (\frac {9-3 x-8 x^2+3 x^3}{-3+3 x^2}\right )\right )}{x^3 \left (9-3 x-17 x^2+6 x^3+8 x^4-3 x^5\right )} \, dx\\ &=2 \int \left (-\frac {4 \left (-36+12 x+71 x^2-26 x^3-38 x^4+12 x^5+3 x^6\right )}{(-1+x) x^3 (1+x) \left (9-3 x-8 x^2+3 x^3\right )}+\frac {\left (-36+12 x+71 x^2-26 x^3-38 x^4+12 x^5+3 x^6\right ) \log \left (\frac {9-3 x-8 x^2+3 x^3}{-3+3 x^2}\right )}{(-1+x) x^2 (1+x) \left (9-3 x-8 x^2+3 x^3\right )}\right ) \, dx\\ &=2 \int \frac {\left (-36+12 x+71 x^2-26 x^3-38 x^4+12 x^5+3 x^6\right ) \log \left (\frac {9-3 x-8 x^2+3 x^3}{-3+3 x^2}\right )}{(-1+x) x^2 (1+x) \left (9-3 x-8 x^2+3 x^3\right )} \, dx-8 \int \frac {-36+12 x+71 x^2-26 x^3-38 x^4+12 x^5+3 x^6}{(-1+x) x^3 (1+x) \left (9-3 x-8 x^2+3 x^3\right )} \, dx\\ &=2 \int \left (\frac {4 \log \left (\frac {9-3 x-8 x^2+3 x^3}{-3+3 x^2}\right )}{x^2}-\frac {2 x \log \left (\frac {9-3 x-8 x^2+3 x^3}{-3+3 x^2}\right )}{-1+x^2}+\frac {\left (-3-16 x+9 x^2\right ) \log \left (\frac {9-3 x-8 x^2+3 x^3}{-3+3 x^2}\right )}{9-3 x-8 x^2+3 x^3}\right ) \, dx-8 \int \left (\frac {1}{1-x}+\frac {4}{x^3}-\frac {1}{3 x}+\frac {1}{1+x}+\frac {-51+19 x+3 x^2}{3 \left (9-3 x-8 x^2+3 x^3\right )}\right ) \, dx\\ &=\frac {16}{x^2}+8 \log (1-x)+\frac {8 \log (x)}{3}-8 \log (1+x)+2 \int \frac {\left (-3-16 x+9 x^2\right ) \log \left (\frac {9-3 x-8 x^2+3 x^3}{-3+3 x^2}\right )}{9-3 x-8 x^2+3 x^3} \, dx-\frac {8}{3} \int \frac {-51+19 x+3 x^2}{9-3 x-8 x^2+3 x^3} \, dx-4 \int \frac {x \log \left (\frac {9-3 x-8 x^2+3 x^3}{-3+3 x^2}\right )}{-1+x^2} \, dx+8 \int \frac {\log \left (\frac {9-3 x-8 x^2+3 x^3}{-3+3 x^2}\right )}{x^2} \, dx\\ &=\frac {16}{x^2}+8 \log (1-x)+\frac {8 \log (x)}{3}-8 \log (1+x)-\frac {8}{9} \log \left (9-3 x-8 x^2+3 x^3\right )-\frac {8 \log \left (-\frac {9-3 x-8 x^2+3 x^3}{3 \left (1-x^2\right )}\right )}{x}-\frac {8}{27} \int \frac {-450+219 x}{9-3 x-8 x^2+3 x^3} \, dx+2 \int \left (-\frac {3 \log \left (\frac {9-3 x-8 x^2+3 x^3}{-3+3 x^2}\right )}{9-3 x-8 x^2+3 x^3}-\frac {16 x \log \left (\frac {9-3 x-8 x^2+3 x^3}{-3+3 x^2}\right )}{9-3 x-8 x^2+3 x^3}+\frac {9 x^2 \log \left (\frac {9-3 x-8 x^2+3 x^3}{-3+3 x^2}\right )}{9-3 x-8 x^2+3 x^3}\right ) \, dx-4 \int \left (\frac {\log \left (\frac {9-3 x-8 x^2+3 x^3}{-3+3 x^2}\right )}{2 (-1+x)}+\frac {\log \left (\frac {9-3 x-8 x^2+3 x^3}{-3+3 x^2}\right )}{2 (1+x)}\right ) \, dx+8 \int \frac {-3+2 x+6 x^2-3 x^4}{x \left (1-x^2\right ) \left (9-3 x-8 x^2+3 x^3\right )} \, dx\\ &=\frac {16}{x^2}+8 \log (1-x)+\frac {8 \log (x)}{3}-8 \log (1+x)-\frac {8}{9} \log \left (9-3 x-8 x^2+3 x^3\right )-\frac {8 \log \left (-\frac {9-3 x-8 x^2+3 x^3}{3 \left (1-x^2\right )}\right )}{x}-\frac {8}{27} \operatorname {Subst}\left (\int \frac {-\frac {766}{3}+219 x}{\frac {515}{243}-\frac {91 x}{9}+3 x^3} \, dx,x,-\frac {8}{9}+x\right )-2 \int \frac {\log \left (\frac {9-3 x-8 x^2+3 x^3}{-3+3 x^2}\right )}{-1+x} \, dx-2 \int \frac {\log \left (\frac {9-3 x-8 x^2+3 x^3}{-3+3 x^2}\right )}{1+x} \, dx-6 \int \frac {\log \left (\frac {9-3 x-8 x^2+3 x^3}{-3+3 x^2}\right )}{9-3 x-8 x^2+3 x^3} \, dx+8 \int \left (\frac {1}{1-x}-\frac {1}{3 x}+\frac {1}{1+x}+\frac {-51+19 x+3 x^2}{3 \left (9-3 x-8 x^2+3 x^3\right )}\right ) \, dx+18 \int \frac {x^2 \log \left (\frac {9-3 x-8 x^2+3 x^3}{-3+3 x^2}\right )}{9-3 x-8 x^2+3 x^3} \, dx-32 \int \frac {x \log \left (\frac {9-3 x-8 x^2+3 x^3}{-3+3 x^2}\right )}{9-3 x-8 x^2+3 x^3} \, dx\\ &=\frac {16}{x^2}-\frac {8}{9} \log \left (9-3 x-8 x^2+3 x^3\right )-\frac {8 \log \left (-\frac {9-3 x-8 x^2+3 x^3}{3 \left (1-x^2\right )}\right )}{x}-2 \log (-1+x) \log \left (-\frac {9-3 x-8 x^2+3 x^3}{3 \left (1-x^2\right )}\right )-2 \log (1+x) \log \left (-\frac {9-3 x-8 x^2+3 x^3}{3 \left (1-x^2\right )}\right )+2 \int \frac {\left (-3+3 x^2\right ) \left (\frac {-3-16 x+9 x^2}{-3+3 x^2}-\frac {6 x \left (9-3 x-8 x^2+3 x^3\right )}{\left (-3+3 x^2\right )^2}\right ) \log (-1+x)}{9-3 x-8 x^2+3 x^3} \, dx+2 \int \frac {\left (-3+3 x^2\right ) \left (\frac {-3-16 x+9 x^2}{-3+3 x^2}-\frac {6 x \left (9-3 x-8 x^2+3 x^3\right )}{\left (-3+3 x^2\right )^2}\right ) \log (1+x)}{9-3 x-8 x^2+3 x^3} \, dx+\frac {8}{3} \int \frac {-51+19 x+3 x^2}{9-3 x-8 x^2+3 x^3} \, dx-\frac {8}{3} \operatorname {Subst}\left (\int \frac {-\frac {766}{3}+219 x}{\left (\frac {182 \sqrt [3]{2}+\left (2 \left (515-81 i \sqrt {419}\right )\right )^{2/3}}{6 \sqrt [3]{515-81 i \sqrt {419}}}+3 x\right ) \left (\frac {1}{9} \left (\left (\frac {1}{2} \left (515-81 i \sqrt {419}\right )\right )^{2/3}-91 \left (1-\frac {91}{\left (\frac {1}{2} \left (515-81 i \sqrt {419}\right )\right )^{2/3}}\right )\right )-\left (\frac {91}{\sqrt [3]{\frac {1}{2} \left (515-81 i \sqrt {419}\right )}}+\sqrt [3]{\frac {1}{2} \left (515-81 i \sqrt {419}\right )}\right ) x+9 x^2\right )} \, dx,x,-\frac {8}{9}+x\right )-6 \int \frac {\log \left (\frac {9-3 x-8 x^2+3 x^3}{-3+3 x^2}\right )}{9-3 x-8 x^2+3 x^3} \, dx+18 \int \frac {x^2 \log \left (\frac {9-3 x-8 x^2+3 x^3}{-3+3 x^2}\right )}{9-3 x-8 x^2+3 x^3} \, dx-32 \int \frac {x \log \left (\frac {9-3 x-8 x^2+3 x^3}{-3+3 x^2}\right )}{9-3 x-8 x^2+3 x^3} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.06, size = 71, normalized size = 2.54 \begin {gather*} 2 \left (\frac {8}{x^2}-\frac {4 \log \left (\frac {9-3 x-8 x^2+3 x^3}{-3+3 x^2}\right )}{x}+\frac {1}{2} \log ^2\left (\frac {9-3 x-8 x^2+3 x^3}{-3+3 x^2}\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(288 - 96*x - 568*x^2 + 208*x^3 + 304*x^4 - 96*x^5 - 24*x^6 + (-72*x + 24*x^2 + 142*x^3 - 52*x^4 - 7
6*x^5 + 24*x^6 + 6*x^7)*Log[(9 - 3*x - 8*x^2 + 3*x^3)/(-3 + 3*x^2)])/(-9*x^3 + 3*x^4 + 17*x^5 - 6*x^6 - 8*x^7
+ 3*x^8),x]

[Out]

2*(8/x^2 - (4*Log[(9 - 3*x - 8*x^2 + 3*x^3)/(-3 + 3*x^2)])/x + Log[(9 - 3*x - 8*x^2 + 3*x^3)/(-3 + 3*x^2)]^2/2
)

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fricas [B]  time = 0.54, size = 65, normalized size = 2.32 \begin {gather*} \frac {x^{2} \log \left (\frac {3 \, x^{3} - 8 \, x^{2} - 3 \, x + 9}{3 \, {\left (x^{2} - 1\right )}}\right )^{2} - 8 \, x \log \left (\frac {3 \, x^{3} - 8 \, x^{2} - 3 \, x + 9}{3 \, {\left (x^{2} - 1\right )}}\right ) + 16}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((6*x^7+24*x^6-76*x^5-52*x^4+142*x^3+24*x^2-72*x)*log((3*x^3-8*x^2-3*x+9)/(3*x^2-3))-24*x^6-96*x^5+3
04*x^4+208*x^3-568*x^2-96*x+288)/(3*x^8-8*x^7-6*x^6+17*x^5+3*x^4-9*x^3),x, algorithm="fricas")

[Out]

(x^2*log(1/3*(3*x^3 - 8*x^2 - 3*x + 9)/(x^2 - 1))^2 - 8*x*log(1/3*(3*x^3 - 8*x^2 - 3*x + 9)/(x^2 - 1)) + 16)/x
^2

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -\frac {2 \, {\left (12 \, x^{6} + 48 \, x^{5} - 152 \, x^{4} - 104 \, x^{3} + 284 \, x^{2} - {\left (3 \, x^{7} + 12 \, x^{6} - 38 \, x^{5} - 26 \, x^{4} + 71 \, x^{3} + 12 \, x^{2} - 36 \, x\right )} \log \left (\frac {3 \, x^{3} - 8 \, x^{2} - 3 \, x + 9}{3 \, {\left (x^{2} - 1\right )}}\right ) + 48 \, x - 144\right )}}{3 \, x^{8} - 8 \, x^{7} - 6 \, x^{6} + 17 \, x^{5} + 3 \, x^{4} - 9 \, x^{3}}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((6*x^7+24*x^6-76*x^5-52*x^4+142*x^3+24*x^2-72*x)*log((3*x^3-8*x^2-3*x+9)/(3*x^2-3))-24*x^6-96*x^5+3
04*x^4+208*x^3-568*x^2-96*x+288)/(3*x^8-8*x^7-6*x^6+17*x^5+3*x^4-9*x^3),x, algorithm="giac")

[Out]

integrate(-2*(12*x^6 + 48*x^5 - 152*x^4 - 104*x^3 + 284*x^2 - (3*x^7 + 12*x^6 - 38*x^5 - 26*x^4 + 71*x^3 + 12*
x^2 - 36*x)*log(1/3*(3*x^3 - 8*x^2 - 3*x + 9)/(x^2 - 1)) + 48*x - 144)/(3*x^8 - 8*x^7 - 6*x^6 + 17*x^5 + 3*x^4
- 9*x^3), x)

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maple [B]  time = 0.48, size = 68, normalized size = 2.43

method	result	size
norman	\(\frac {16+x^{2} \ln \left (\frac {3 x^{3}-8 x^{2}-3 x +9}{3 x^{2}-3}\right )^{2}-8 x \ln \left (\frac {3 x^{3}-8 x^{2}-3 x +9}{3 x^{2}-3}\right )}{x^{2}}\)	\(68\)
default	\(-\ln \left (x +1\right )^{2}+\frac {16}{x^{2}}+\frac {8 \ln \relax (3)}{x}-\ln \left (x -1\right )^{2}-2 \ln \left (x -1\right ) \ln \left (\frac {x}{2}+\frac {1}{2}\right )-2 \ln \left (x -1\right ) \ln \left (\frac {3 x^{3}-8 x^{2}-3 x +9}{x^{2}-1}\right )-2 \left (\ln \left (x +1\right )-\ln \left (\frac {x}{2}+\frac {1}{2}\right )\right ) \ln \left (-\frac {x}{2}+\frac {1}{2}\right )-2 \ln \left (x +1\right ) \ln \left (\frac {3 x^{3}-8 x^{2}-3 x +9}{x^{2}-1}\right )-2 \ln \relax (3) \ln \left (3 x^{3}-8 x^{2}-3 x +9\right )+2 \ln \relax (3) \ln \left (x -1\right )+2 \ln \relax (3) \ln \left (x +1\right )+2 \left (\munderset {\underline {\hspace {1.25 ex}}\alpha =\RootOf \left (3 \textit {\_Z}^{3}-8 \textit {\_Z}^{2}-3 \textit {\_Z} +9\right )}{\sum }\left (\ln \left (x -\underline {\hspace {1.25 ex}}\alpha \right ) \ln \left (\frac {3 x^{3}-8 x^{2}-3 x +9}{x^{2}-1}\right )-\frac {\ln \left (x -\underline {\hspace {1.25 ex}}\alpha \right )^{2}}{2}-\ln \left (x -\underline {\hspace {1.25 ex}}\alpha \right ) \ln \left (\frac {-3 \underline {\hspace {1.25 ex}}\alpha +8+\sqrt {-27 \underline {\hspace {1.25 ex}}\alpha ^{2}+48 \underline {\hspace {1.25 ex}}\alpha +100}-6 x}{-9 \underline {\hspace {1.25 ex}}\alpha +8+\sqrt {-27 \underline {\hspace {1.25 ex}}\alpha ^{2}+48 \underline {\hspace {1.25 ex}}\alpha +100}}\right )-\ln \left (x -\underline {\hspace {1.25 ex}}\alpha \right ) \ln \left (\frac {3 \underline {\hspace {1.25 ex}}\alpha -8+\sqrt {-27 \underline {\hspace {1.25 ex}}\alpha ^{2}+48 \underline {\hspace {1.25 ex}}\alpha +100}+6 x}{9 \underline {\hspace {1.25 ex}}\alpha -8+\sqrt {-27 \underline {\hspace {1.25 ex}}\alpha ^{2}+48 \underline {\hspace {1.25 ex}}\alpha +100}}\right )-\dilog \left (\frac {-3 \underline {\hspace {1.25 ex}}\alpha +8+\sqrt {-27 \underline {\hspace {1.25 ex}}\alpha ^{2}+48 \underline {\hspace {1.25 ex}}\alpha +100}-6 x}{-9 \underline {\hspace {1.25 ex}}\alpha +8+\sqrt {-27 \underline {\hspace {1.25 ex}}\alpha ^{2}+48 \underline {\hspace {1.25 ex}}\alpha +100}}\right )-\dilog \left (\frac {3 \underline {\hspace {1.25 ex}}\alpha -8+\sqrt {-27 \underline {\hspace {1.25 ex}}\alpha ^{2}+48 \underline {\hspace {1.25 ex}}\alpha +100}+6 x}{9 \underline {\hspace {1.25 ex}}\alpha -8+\sqrt {-27 \underline {\hspace {1.25 ex}}\alpha ^{2}+48 \underline {\hspace {1.25 ex}}\alpha +100}}\right )+\dilog \left (\frac {x -1}{\underline {\hspace {1.25 ex}}\alpha -1}\right )+\ln \left (x -\underline {\hspace {1.25 ex}}\alpha \right ) \ln \left (\frac {x -1}{\underline {\hspace {1.25 ex}}\alpha -1}\right )+\dilog \left (\frac {x +1}{\underline {\hspace {1.25 ex}}\alpha +1}\right )+\ln \left (x -\underline {\hspace {1.25 ex}}\alpha \right ) \ln \left (\frac {x +1}{\underline {\hspace {1.25 ex}}\alpha +1}\right )\right )\right )+2 \dilog \left (\frac {\RootOf \left (3 \textit {\_Z}^{3}-17 \textit {\_Z}^{2}+22 \textit {\_Z} +1, \mathit {index} =3\right )-x -1}{\RootOf \left (3 \textit {\_Z}^{3}-17 \textit {\_Z}^{2}+22 \textit {\_Z} +1, \mathit {index} =3\right )}\right )+2 \dilog \left (\frac {\RootOf \left (3 \textit {\_Z}^{3}-17 \textit {\_Z}^{2}+22 \textit {\_Z} +1, \mathit {index} =1\right )-x -1}{\RootOf \left (3 \textit {\_Z}^{3}-17 \textit {\_Z}^{2}+22 \textit {\_Z} +1, \mathit {index} =1\right )}\right )+2 \dilog \left (\frac {\RootOf \left (3 \textit {\_Z}^{3}-17 \textit {\_Z}^{2}+22 \textit {\_Z} +1, \mathit {index} =2\right )-x -1}{\RootOf \left (3 \textit {\_Z}^{3}-17 \textit {\_Z}^{2}+22 \textit {\_Z} +1, \mathit {index} =2\right )}\right )+2 \dilog \left (\frac {\RootOf \left (3 \textit {\_Z}^{3}+\textit {\_Z}^{2}-10 \textit {\_Z} +1, \mathit {index} =1\right )-x +1}{\RootOf \left (3 \textit {\_Z}^{3}+\textit {\_Z}^{2}-10 \textit {\_Z} +1, \mathit {index} =1\right )}\right )+2 \dilog \left (\frac {\RootOf \left (3 \textit {\_Z}^{3}+\textit {\_Z}^{2}-10 \textit {\_Z} +1, \mathit {index} =2\right )-x +1}{\RootOf \left (3 \textit {\_Z}^{3}+\textit {\_Z}^{2}-10 \textit {\_Z} +1, \mathit {index} =2\right )}\right )+2 \dilog \left (\frac {\RootOf \left (3 \textit {\_Z}^{3}+\textit {\_Z}^{2}-10 \textit {\_Z} +1, \mathit {index} =3\right )-x +1}{\RootOf \left (3 \textit {\_Z}^{3}+\textit {\_Z}^{2}-10 \textit {\_Z} +1, \mathit {index} =3\right )}\right )+2 \ln \left (x -1\right ) \ln \left (\frac {\RootOf \left (3 \textit {\_Z}^{3}+\textit {\_Z}^{2}-10 \textit {\_Z} +1, \mathit {index} =1\right )-x +1}{\RootOf \left (3 \textit {\_Z}^{3}+\textit {\_Z}^{2}-10 \textit {\_Z} +1, \mathit {index} =1\right )}\right )+2 \ln \left (x -1\right ) \ln \left (\frac {\RootOf \left (3 \textit {\_Z}^{3}+\textit {\_Z}^{2}-10 \textit {\_Z} +1, \mathit {index} =2\right )-x +1}{\RootOf \left (3 \textit {\_Z}^{3}+\textit {\_Z}^{2}-10 \textit {\_Z} +1, \mathit {index} =2\right )}\right )+2 \ln \left (x -1\right ) \ln \left (\frac {\RootOf \left (3 \textit {\_Z}^{3}+\textit {\_Z}^{2}-10 \textit {\_Z} +1, \mathit {index} =3\right )-x +1}{\RootOf \left (3 \textit {\_Z}^{3}+\textit {\_Z}^{2}-10 \textit {\_Z} +1, \mathit {index} =3\right )}\right )+2 \ln \left (x +1\right ) \ln \left (\frac {\RootOf \left (3 \textit {\_Z}^{3}-17 \textit {\_Z}^{2}+22 \textit {\_Z} +1, \mathit {index} =1\right )-x -1}{\RootOf \left (3 \textit {\_Z}^{3}-17 \textit {\_Z}^{2}+22 \textit {\_Z} +1, \mathit {index} =1\right )}\right )+2 \ln \left (x +1\right ) \ln \left (\frac {\RootOf \left (3 \textit {\_Z}^{3}-17 \textit {\_Z}^{2}+22 \textit {\_Z} +1, \mathit {index} =2\right )-x -1}{\RootOf \left (3 \textit {\_Z}^{3}-17 \textit {\_Z}^{2}+22 \textit {\_Z} +1, \mathit {index} =2\right )}\right )+2 \ln \left (x +1\right ) \ln \left (\frac {\RootOf \left (3 \textit {\_Z}^{3}-17 \textit {\_Z}^{2}+22 \textit {\_Z} +1, \mathit {index} =3\right )-x -1}{\RootOf \left (3 \textit {\_Z}^{3}-17 \textit {\_Z}^{2}+22 \textit {\_Z} +1, \mathit {index} =3\right )}\right )-\frac {8 \ln \left (\frac {3 x^{3}-8 x^{2}-3 x +9}{x^{2}-1}\right )}{x}\)	\(1077\)
risch	\(\text {Expression too large to display}\)	\(6674\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((6*x^7+24*x^6-76*x^5-52*x^4+142*x^3+24*x^2-72*x)*ln((3*x^3-8*x^2-3*x+9)/(3*x^2-3))-24*x^6-96*x^5+304*x^4+
208*x^3-568*x^2-96*x+288)/(3*x^8-8*x^7-6*x^6+17*x^5+3*x^4-9*x^3),x,method=_RETURNVERBOSE)

[Out]

(16+x^2*ln((3*x^3-8*x^2-3*x+9)/(3*x^2-3))^2-8*x*ln((3*x^3-8*x^2-3*x+9)/(3*x^2-3)))/x^2

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maxima [B]  time = 0.61, size = 137, normalized size = 4.89 \begin {gather*} \frac {x^{2} \log \left (3 \, x^{3} - 8 \, x^{2} - 3 \, x + 9\right )^{2} + x^{2} \log \left (x + 1\right )^{2} + x^{2} \log \left (x - 1\right )^{2} + 8 \, x \log \relax (3) - 2 \, {\left (x^{2} \log \relax (3) + x^{2} \log \left (x + 1\right ) + x^{2} \log \left (x - 1\right ) + 4 \, x\right )} \log \left (3 \, x^{3} - 8 \, x^{2} - 3 \, x + 9\right ) + 2 \, {\left (x^{2} \log \relax (3) + x^{2} \log \left (x - 1\right ) + 4 \, x\right )} \log \left (x + 1\right ) + 2 \, {\left (x^{2} \log \relax (3) + 4 \, x\right )} \log \left (x - 1\right ) + 16}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((6*x^7+24*x^6-76*x^5-52*x^4+142*x^3+24*x^2-72*x)*log((3*x^3-8*x^2-3*x+9)/(3*x^2-3))-24*x^6-96*x^5+3
04*x^4+208*x^3-568*x^2-96*x+288)/(3*x^8-8*x^7-6*x^6+17*x^5+3*x^4-9*x^3),x, algorithm="maxima")

[Out]

(x^2*log(3*x^3 - 8*x^2 - 3*x + 9)^2 + x^2*log(x + 1)^2 + x^2*log(x - 1)^2 + 8*x*log(3) - 2*(x^2*log(3) + x^2*l
og(x + 1) + x^2*log(x - 1) + 4*x)*log(3*x^3 - 8*x^2 - 3*x + 9) + 2*(x^2*log(3) + x^2*log(x - 1) + 4*x)*log(x +
1) + 2*(x^2*log(3) + 4*x)*log(x - 1) + 16)/x^2

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mupad [B]  time = 2.11, size = 37, normalized size = 1.32 \begin {gather*} \frac {{\left (x\,\ln \left (-\frac {-3\,x^3+8\,x^2+3\,x-9}{3\,x^2-3}\right )-4\right )}^2}{x^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((96*x - log(-(3*x + 8*x^2 - 3*x^3 - 9)/(3*x^2 - 3))*(24*x^2 - 72*x + 142*x^3 - 52*x^4 - 76*x^5 + 24*x^6 +
6*x^7) + 568*x^2 - 208*x^3 - 304*x^4 + 96*x^5 + 24*x^6 - 288)/(9*x^3 - 3*x^4 - 17*x^5 + 6*x^6 + 8*x^7 - 3*x^8)
,x)

[Out]

(x*log(-(3*x + 8*x^2 - 3*x^3 - 9)/(3*x^2 - 3)) - 4)^2/x^2

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sympy [B]  time = 0.28, size = 56, normalized size = 2.00 \begin {gather*} \log {\left (\frac {3 x^{3} - 8 x^{2} - 3 x + 9}{3 x^{2} - 3} \right )}^{2} - \frac {8 \log {\left (\frac {3 x^{3} - 8 x^{2} - 3 x + 9}{3 x^{2} - 3} \right )}}{x} + \frac {16}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((6*x**7+24*x**6-76*x**5-52*x**4+142*x**3+24*x**2-72*x)*ln((3*x**3-8*x**2-3*x+9)/(3*x**2-3))-24*x**6
-96*x**5+304*x**4+208*x**3-568*x**2-96*x+288)/(3*x**8-8*x**7-6*x**6+17*x**5+3*x**4-9*x**3),x)

[Out]

log((3*x**3 - 8*x**2 - 3*x + 9)/(3*x**2 - 3))**2 - 8*log((3*x**3 - 8*x**2 - 3*x + 9)/(3*x**2 - 3))/x + 16/x**2

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