3.94.50 \(\int \frac {(38+6 x) \log (\frac {-1875+475 x+47 x^2+x^3}{-5624+1425 x+141 x^2+3 x^3})}{421800-230603 x+15151 x^2+4302 x^3+207 x^4+3 x^5} \, dx\)

Optimal. Leaf size=23 \[ \log ^2\left (\frac {1}{3+\frac {x}{(25+x)^2 \left (-3 x+x^2\right )}}\right ) \]

________________________________________________________________________________________

Rubi [F]  time = 20.13, 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 {(38+6 x) \log \left (\frac {-1875+475 x+47 x^2+x^3}{-5624+1425 x+141 x^2+3 x^3}\right )}{421800-230603 x+15151 x^2+4302 x^3+207 x^4+3 x^5} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[((38 + 6*x)*Log[(-1875 + 475*x + 47*x^2 + x^3)/(-5624 + 1425*x + 141*x^2 + 3*x^3)])/(421800 - 230603*x + 1
5151*x^2 + 4302*x^3 + 207*x^4 + 3*x^5),x]

[Out]

-Log[-3 + x]^2 - 4*Log[-3 + x]*Log[(25 + x)/28] - 4*Log[(3 - x)/28]*Log[25 + x] - 4*Log[25 + x]^2 + 2*Log[-3 +
x]*Log[(1875 - 475*x - 47*x^2 - x^3)/(5624 - 1425*x - 141*x^2 - 3*x^3)] + 4*Log[25 + x]*Log[(1875 - 475*x - 4
7*x^2 - x^3)/(5624 - 1425*x - 141*x^2 - 3*x^3)] - 4*PolyLog[2, (3 - x)/28] - 4*PolyLog[2, (25 + x)/28] + 2850*
Defer[Int][Log[-3 + x]/(-5624 + 1425*x + 141*x^2 + 3*x^3), x] + 564*Defer[Int][(x*Log[-3 + x])/(-5624 + 1425*x
+ 141*x^2 + 3*x^3), x] + 18*Defer[Int][(x^2*Log[-3 + x])/(-5624 + 1425*x + 141*x^2 + 3*x^3), x] + 5700*Defer[
Int][Log[25 + x]/(-5624 + 1425*x + 141*x^2 + 3*x^3), x] + 1128*Defer[Int][(x*Log[25 + x])/(-5624 + 1425*x + 14
1*x^2 + 3*x^3), x] + 36*Defer[Int][(x^2*Log[25 + x])/(-5624 + 1425*x + 141*x^2 + 3*x^3), x] - 2850*Defer[Int][
Log[(-1875 + 475*x + 47*x^2 + x^3)/(-5624 + 1425*x + 141*x^2 + 3*x^3)]/(-5624 + 1425*x + 141*x^2 + 3*x^3), x]
- 564*Defer[Int][(x*Log[(-1875 + 475*x + 47*x^2 + x^3)/(-5624 + 1425*x + 141*x^2 + 3*x^3)])/(-5624 + 1425*x +
141*x^2 + 3*x^3), x] - 18*Defer[Int][(x^2*Log[(-1875 + 475*x + 47*x^2 + x^3)/(-5624 + 1425*x + 141*x^2 + 3*x^3
)])/(-5624 + 1425*x + 141*x^2 + 3*x^3), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {2 \log \left (\frac {-1875+475 x+47 x^2+x^3}{-5624+1425 x+141 x^2+3 x^3}\right )}{-3+x}+\frac {4 \log \left (\frac {-1875+475 x+47 x^2+x^3}{-5624+1425 x+141 x^2+3 x^3}\right )}{25+x}-\frac {6 \left (475+94 x+3 x^2\right ) \log \left (\frac {-1875+475 x+47 x^2+x^3}{-5624+1425 x+141 x^2+3 x^3}\right )}{-5624+1425 x+141 x^2+3 x^3}\right ) \, dx\\ &=2 \int \frac {\log \left (\frac {-1875+475 x+47 x^2+x^3}{-5624+1425 x+141 x^2+3 x^3}\right )}{-3+x} \, dx+4 \int \frac {\log \left (\frac {-1875+475 x+47 x^2+x^3}{-5624+1425 x+141 x^2+3 x^3}\right )}{25+x} \, dx-6 \int \frac {\left (475+94 x+3 x^2\right ) \log \left (\frac {-1875+475 x+47 x^2+x^3}{-5624+1425 x+141 x^2+3 x^3}\right )}{-5624+1425 x+141 x^2+3 x^3} \, dx\\ &=2 \log (-3+x) \log \left (\frac {1875-475 x-47 x^2-x^3}{5624-1425 x-141 x^2-3 x^3}\right )+4 \log (25+x) \log \left (\frac {1875-475 x-47 x^2-x^3}{5624-1425 x-141 x^2-3 x^3}\right )-2 \int \frac {\left (-5624+1425 x+141 x^2+3 x^3\right ) \left (-\frac {\left (1425+282 x+9 x^2\right ) \left (-1875+475 x+47 x^2+x^3\right )}{\left (-5624+1425 x+141 x^2+3 x^3\right )^2}+\frac {475+94 x+3 x^2}{-5624+1425 x+141 x^2+3 x^3}\right ) \log (-3+x)}{-1875+475 x+47 x^2+x^3} \, dx-4 \int \frac {\left (-5624+1425 x+141 x^2+3 x^3\right ) \left (-\frac {\left (1425+282 x+9 x^2\right ) \left (-1875+475 x+47 x^2+x^3\right )}{\left (-5624+1425 x+141 x^2+3 x^3\right )^2}+\frac {475+94 x+3 x^2}{-5624+1425 x+141 x^2+3 x^3}\right ) \log (25+x)}{-1875+475 x+47 x^2+x^3} \, dx-6 \int \left (\frac {475 \log \left (\frac {-1875+475 x+47 x^2+x^3}{-5624+1425 x+141 x^2+3 x^3}\right )}{-5624+1425 x+141 x^2+3 x^3}+\frac {94 x \log \left (\frac {-1875+475 x+47 x^2+x^3}{-5624+1425 x+141 x^2+3 x^3}\right )}{-5624+1425 x+141 x^2+3 x^3}+\frac {3 x^2 \log \left (\frac {-1875+475 x+47 x^2+x^3}{-5624+1425 x+141 x^2+3 x^3}\right )}{-5624+1425 x+141 x^2+3 x^3}\right ) \, dx\\ &=2 \log (-3+x) \log \left (\frac {1875-475 x-47 x^2-x^3}{5624-1425 x-141 x^2-3 x^3}\right )+4 \log (25+x) \log \left (\frac {1875-475 x-47 x^2-x^3}{5624-1425 x-141 x^2-3 x^3}\right )-2 \int \left (\frac {\log (-3+x)}{-3+x}+\frac {2 \log (-3+x)}{25+x}-\frac {3 \left (475+94 x+3 x^2\right ) \log (-3+x)}{-5624+1425 x+141 x^2+3 x^3}\right ) \, dx-4 \int \left (\frac {\log (25+x)}{-3+x}+\frac {2 \log (25+x)}{25+x}-\frac {3 \left (475+94 x+3 x^2\right ) \log (25+x)}{-5624+1425 x+141 x^2+3 x^3}\right ) \, dx-18 \int \frac {x^2 \log \left (\frac {-1875+475 x+47 x^2+x^3}{-5624+1425 x+141 x^2+3 x^3}\right )}{-5624+1425 x+141 x^2+3 x^3} \, dx-564 \int \frac {x \log \left (\frac {-1875+475 x+47 x^2+x^3}{-5624+1425 x+141 x^2+3 x^3}\right )}{-5624+1425 x+141 x^2+3 x^3} \, dx-2850 \int \frac {\log \left (\frac {-1875+475 x+47 x^2+x^3}{-5624+1425 x+141 x^2+3 x^3}\right )}{-5624+1425 x+141 x^2+3 x^3} \, dx\\ &=2 \log (-3+x) \log \left (\frac {1875-475 x-47 x^2-x^3}{5624-1425 x-141 x^2-3 x^3}\right )+4 \log (25+x) \log \left (\frac {1875-475 x-47 x^2-x^3}{5624-1425 x-141 x^2-3 x^3}\right )-2 \int \frac {\log (-3+x)}{-3+x} \, dx-4 \int \frac {\log (-3+x)}{25+x} \, dx-4 \int \frac {\log (25+x)}{-3+x} \, dx+6 \int \frac {\left (475+94 x+3 x^2\right ) \log (-3+x)}{-5624+1425 x+141 x^2+3 x^3} \, dx-8 \int \frac {\log (25+x)}{25+x} \, dx+12 \int \frac {\left (475+94 x+3 x^2\right ) \log (25+x)}{-5624+1425 x+141 x^2+3 x^3} \, dx-18 \int \frac {x^2 \log \left (\frac {-1875+475 x+47 x^2+x^3}{-5624+1425 x+141 x^2+3 x^3}\right )}{-5624+1425 x+141 x^2+3 x^3} \, dx-564 \int \frac {x \log \left (\frac {-1875+475 x+47 x^2+x^3}{-5624+1425 x+141 x^2+3 x^3}\right )}{-5624+1425 x+141 x^2+3 x^3} \, dx-2850 \int \frac {\log \left (\frac {-1875+475 x+47 x^2+x^3}{-5624+1425 x+141 x^2+3 x^3}\right )}{-5624+1425 x+141 x^2+3 x^3} \, dx\\ &=-4 \log (-3+x) \log \left (\frac {25+x}{28}\right )-4 \log \left (\frac {3-x}{28}\right ) \log (25+x)+2 \log (-3+x) \log \left (\frac {1875-475 x-47 x^2-x^3}{5624-1425 x-141 x^2-3 x^3}\right )+4 \log (25+x) \log \left (\frac {1875-475 x-47 x^2-x^3}{5624-1425 x-141 x^2-3 x^3}\right )-2 \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,-3+x\right )+4 \int \frac {\log \left (\frac {3-x}{28}\right )}{25+x} \, dx+4 \int \frac {\log \left (\frac {25+x}{28}\right )}{-3+x} \, dx+6 \int \left (\frac {475 \log (-3+x)}{-5624+1425 x+141 x^2+3 x^3}+\frac {94 x \log (-3+x)}{-5624+1425 x+141 x^2+3 x^3}+\frac {3 x^2 \log (-3+x)}{-5624+1425 x+141 x^2+3 x^3}\right ) \, dx-8 \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,25+x\right )+12 \int \left (\frac {475 \log (25+x)}{-5624+1425 x+141 x^2+3 x^3}+\frac {94 x \log (25+x)}{-5624+1425 x+141 x^2+3 x^3}+\frac {3 x^2 \log (25+x)}{-5624+1425 x+141 x^2+3 x^3}\right ) \, dx-18 \int \frac {x^2 \log \left (\frac {-1875+475 x+47 x^2+x^3}{-5624+1425 x+141 x^2+3 x^3}\right )}{-5624+1425 x+141 x^2+3 x^3} \, dx-564 \int \frac {x \log \left (\frac {-1875+475 x+47 x^2+x^3}{-5624+1425 x+141 x^2+3 x^3}\right )}{-5624+1425 x+141 x^2+3 x^3} \, dx-2850 \int \frac {\log \left (\frac {-1875+475 x+47 x^2+x^3}{-5624+1425 x+141 x^2+3 x^3}\right )}{-5624+1425 x+141 x^2+3 x^3} \, dx\\ &=-\log ^2(-3+x)-4 \log (-3+x) \log \left (\frac {25+x}{28}\right )-4 \log \left (\frac {3-x}{28}\right ) \log (25+x)-4 \log ^2(25+x)+2 \log (-3+x) \log \left (\frac {1875-475 x-47 x^2-x^3}{5624-1425 x-141 x^2-3 x^3}\right )+4 \log (25+x) \log \left (\frac {1875-475 x-47 x^2-x^3}{5624-1425 x-141 x^2-3 x^3}\right )+4 \operatorname {Subst}\left (\int \frac {\log \left (1-\frac {x}{28}\right )}{x} \, dx,x,25+x\right )+4 \operatorname {Subst}\left (\int \frac {\log \left (1+\frac {x}{28}\right )}{x} \, dx,x,-3+x\right )+18 \int \frac {x^2 \log (-3+x)}{-5624+1425 x+141 x^2+3 x^3} \, dx-18 \int \frac {x^2 \log \left (\frac {-1875+475 x+47 x^2+x^3}{-5624+1425 x+141 x^2+3 x^3}\right )}{-5624+1425 x+141 x^2+3 x^3} \, dx+36 \int \frac {x^2 \log (25+x)}{-5624+1425 x+141 x^2+3 x^3} \, dx+564 \int \frac {x \log (-3+x)}{-5624+1425 x+141 x^2+3 x^3} \, dx-564 \int \frac {x \log \left (\frac {-1875+475 x+47 x^2+x^3}{-5624+1425 x+141 x^2+3 x^3}\right )}{-5624+1425 x+141 x^2+3 x^3} \, dx+1128 \int \frac {x \log (25+x)}{-5624+1425 x+141 x^2+3 x^3} \, dx+2850 \int \frac {\log (-3+x)}{-5624+1425 x+141 x^2+3 x^3} \, dx-2850 \int \frac {\log \left (\frac {-1875+475 x+47 x^2+x^3}{-5624+1425 x+141 x^2+3 x^3}\right )}{-5624+1425 x+141 x^2+3 x^3} \, dx+5700 \int \frac {\log (25+x)}{-5624+1425 x+141 x^2+3 x^3} \, dx\\ &=-\log ^2(-3+x)-4 \log (-3+x) \log \left (\frac {25+x}{28}\right )-4 \log \left (\frac {3-x}{28}\right ) \log (25+x)-4 \log ^2(25+x)+2 \log (-3+x) \log \left (\frac {1875-475 x-47 x^2-x^3}{5624-1425 x-141 x^2-3 x^3}\right )+4 \log (25+x) \log \left (\frac {1875-475 x-47 x^2-x^3}{5624-1425 x-141 x^2-3 x^3}\right )-4 \text {Li}_2\left (\frac {3-x}{28}\right )-4 \text {Li}_2\left (\frac {25+x}{28}\right )+18 \int \frac {x^2 \log (-3+x)}{-5624+1425 x+141 x^2+3 x^3} \, dx-18 \int \frac {x^2 \log \left (\frac {-1875+475 x+47 x^2+x^3}{-5624+1425 x+141 x^2+3 x^3}\right )}{-5624+1425 x+141 x^2+3 x^3} \, dx+36 \int \frac {x^2 \log (25+x)}{-5624+1425 x+141 x^2+3 x^3} \, dx+564 \int \frac {x \log (-3+x)}{-5624+1425 x+141 x^2+3 x^3} \, dx-564 \int \frac {x \log \left (\frac {-1875+475 x+47 x^2+x^3}{-5624+1425 x+141 x^2+3 x^3}\right )}{-5624+1425 x+141 x^2+3 x^3} \, dx+1128 \int \frac {x \log (25+x)}{-5624+1425 x+141 x^2+3 x^3} \, dx+2850 \int \frac {\log (-3+x)}{-5624+1425 x+141 x^2+3 x^3} \, dx-2850 \int \frac {\log \left (\frac {-1875+475 x+47 x^2+x^3}{-5624+1425 x+141 x^2+3 x^3}\right )}{-5624+1425 x+141 x^2+3 x^3} \, dx+5700 \int \frac {\log (25+x)}{-5624+1425 x+141 x^2+3 x^3} \, dx\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.27, size = 29, normalized size = 1.26 \begin {gather*} \log ^2\left (\frac {(-3+x) (25+x)^2}{-5624+1425 x+141 x^2+3 x^3}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[((38 + 6*x)*Log[(-1875 + 475*x + 47*x^2 + x^3)/(-5624 + 1425*x + 141*x^2 + 3*x^3)])/(421800 - 230603
*x + 15151*x^2 + 4302*x^3 + 207*x^4 + 3*x^5),x]

[Out]

Log[((-3 + x)*(25 + x)^2)/(-5624 + 1425*x + 141*x^2 + 3*x^3)]^2

________________________________________________________________________________________

fricas [A]  time = 0.75, size = 34, normalized size = 1.48 \begin {gather*} \log \left (\frac {x^{3} + 47 \, x^{2} + 475 \, x - 1875}{3 \, x^{3} + 141 \, x^{2} + 1425 \, x - 5624}\right )^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((6*x+38)*log((x^3+47*x^2+475*x-1875)/(3*x^3+141*x^2+1425*x-5624))/(3*x^5+207*x^4+4302*x^3+15151*x^2-
230603*x+421800),x, algorithm="fricas")

[Out]

log((x^3 + 47*x^2 + 475*x - 1875)/(3*x^3 + 141*x^2 + 1425*x - 5624))^2

________________________________________________________________________________________

giac [A]  time = 0.22, size = 34, normalized size = 1.48 \begin {gather*} \log \left (\frac {x^{3} + 47 \, x^{2} + 475 \, x - 1875}{3 \, x^{3} + 141 \, x^{2} + 1425 \, x - 5624}\right )^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((6*x+38)*log((x^3+47*x^2+475*x-1875)/(3*x^3+141*x^2+1425*x-5624))/(3*x^5+207*x^4+4302*x^3+15151*x^2-
230603*x+421800),x, algorithm="giac")

[Out]

log((x^3 + 47*x^2 + 475*x - 1875)/(3*x^3 + 141*x^2 + 1425*x - 5624))^2

________________________________________________________________________________________

maple [A]  time = 0.45, size = 35, normalized size = 1.52

method	result	size
norman	\(\ln \left (\frac {x^{3}+47 x^{2}+475 x -1875}{3 x^{3}+141 x^{2}+1425 x -5624}\right )^{2}\)	\(35\)
default	\(2 \ln \left (x -3\right ) \ln \left (\frac {x^{3}+47 x^{2}+475 x -1875}{3 x^{3}+141 x^{2}+1425 x -5624}\right )-4 \ln \left (x -3\right ) \ln \left (\frac {x}{28}+\frac {25}{28}\right )+2 \ln \left (x -3\right ) \ln \left (\frac {\RootOf \left (3 \textit {\_Z}^{3}+168 \textit {\_Z}^{2}+2352 \textit {\_Z} +1, \mathit {index} =1\right )-x +3}{\RootOf \left (3 \textit {\_Z}^{3}+168 \textit {\_Z}^{2}+2352 \textit {\_Z} +1, \mathit {index} =1\right )}\right )+2 \dilog \left (\frac {\RootOf \left (3 \textit {\_Z}^{3}+168 \textit {\_Z}^{2}+2352 \textit {\_Z} +1, \mathit {index} =1\right )-x +3}{\RootOf \left (3 \textit {\_Z}^{3}+168 \textit {\_Z}^{2}+2352 \textit {\_Z} +1, \mathit {index} =1\right )}\right )+2 \ln \left (x -3\right ) \ln \left (\frac {\RootOf \left (3 \textit {\_Z}^{3}+168 \textit {\_Z}^{2}+2352 \textit {\_Z} +1, \mathit {index} =2\right )-x +3}{\RootOf \left (3 \textit {\_Z}^{3}+168 \textit {\_Z}^{2}+2352 \textit {\_Z} +1, \mathit {index} =2\right )}\right )+2 \dilog \left (\frac {\RootOf \left (3 \textit {\_Z}^{3}+168 \textit {\_Z}^{2}+2352 \textit {\_Z} +1, \mathit {index} =2\right )-x +3}{\RootOf \left (3 \textit {\_Z}^{3}+168 \textit {\_Z}^{2}+2352 \textit {\_Z} +1, \mathit {index} =2\right )}\right )+2 \ln \left (x -3\right ) \ln \left (\frac {\RootOf \left (3 \textit {\_Z}^{3}+168 \textit {\_Z}^{2}+2352 \textit {\_Z} +1, \mathit {index} =3\right )-x +3}{\RootOf \left (3 \textit {\_Z}^{3}+168 \textit {\_Z}^{2}+2352 \textit {\_Z} +1, \mathit {index} =3\right )}\right )+2 \dilog \left (\frac {\RootOf \left (3 \textit {\_Z}^{3}+168 \textit {\_Z}^{2}+2352 \textit {\_Z} +1, \mathit {index} =3\right )-x +3}{\RootOf \left (3 \textit {\_Z}^{3}+168 \textit {\_Z}^{2}+2352 \textit {\_Z} +1, \mathit {index} =3\right )}\right )-\ln \left (x -3\right )^{2}+2 \left (\munderset {\underline {\hspace {1.25 ex}}\alpha =\RootOf \left (3 \textit {\_Z}^{3}+141 \textit {\_Z}^{2}+1425 \textit {\_Z} -5624\right )}{\sum }\left (-\ln \left (x -\underline {\hspace {1.25 ex}}\alpha \right ) \ln \left (\frac {x^{3}+47 x^{2}+475 x -1875}{3 x^{3}+141 x^{2}+1425 x -5624}\right )-\ln \left (x -\underline {\hspace {1.25 ex}}\alpha \right ) \ln \left (\frac {\underline {\hspace {1.25 ex}}\alpha +47-\sqrt {-3 \underline {\hspace {1.25 ex}}\alpha ^{2}-94 \underline {\hspace {1.25 ex}}\alpha +309}+2 x}{3 \underline {\hspace {1.25 ex}}\alpha +47-\sqrt {-3 \underline {\hspace {1.25 ex}}\alpha ^{2}-94 \underline {\hspace {1.25 ex}}\alpha +309}}\right )-\ln \left (x -\underline {\hspace {1.25 ex}}\alpha \right ) \ln \left (\frac {\underline {\hspace {1.25 ex}}\alpha +47+\sqrt {-3 \underline {\hspace {1.25 ex}}\alpha ^{2}-94 \underline {\hspace {1.25 ex}}\alpha +309}+2 x}{3 \underline {\hspace {1.25 ex}}\alpha +47+\sqrt {-3 \underline {\hspace {1.25 ex}}\alpha ^{2}-94 \underline {\hspace {1.25 ex}}\alpha +309}}\right )-\dilog \left (\frac {\underline {\hspace {1.25 ex}}\alpha +47-\sqrt {-3 \underline {\hspace {1.25 ex}}\alpha ^{2}-94 \underline {\hspace {1.25 ex}}\alpha +309}+2 x}{3 \underline {\hspace {1.25 ex}}\alpha +47-\sqrt {-3 \underline {\hspace {1.25 ex}}\alpha ^{2}-94 \underline {\hspace {1.25 ex}}\alpha +309}}\right )-\dilog \left (\frac {\underline {\hspace {1.25 ex}}\alpha +47+\sqrt {-3 \underline {\hspace {1.25 ex}}\alpha ^{2}-94 \underline {\hspace {1.25 ex}}\alpha +309}+2 x}{3 \underline {\hspace {1.25 ex}}\alpha +47+\sqrt {-3 \underline {\hspace {1.25 ex}}\alpha ^{2}-94 \underline {\hspace {1.25 ex}}\alpha +309}}\right )+2 \dilog \left (\frac {x +25}{25+\underline {\hspace {1.25 ex}}\alpha }\right )+2 \ln \left (x -\underline {\hspace {1.25 ex}}\alpha \right ) \ln \left (\frac {x +25}{25+\underline {\hspace {1.25 ex}}\alpha }\right )+\dilog \left (\frac {x -3}{\underline {\hspace {1.25 ex}}\alpha -3}\right )+\ln \left (x -\underline {\hspace {1.25 ex}}\alpha \right ) \ln \left (\frac {x -3}{\underline {\hspace {1.25 ex}}\alpha -3}\right )-\frac {\ln \left (x -\underline {\hspace {1.25 ex}}\alpha \right )^{2}}{2}\right )\right )+4 \ln \left (x +25\right ) \ln \left (\frac {x^{3}+47 x^{2}+475 x -1875}{3 x^{3}+141 x^{2}+1425 x -5624}\right )-4 \left (\ln \left (x +25\right )-\ln \left (\frac {x}{28}+\frac {25}{28}\right )\right ) \ln \left (-\frac {x}{28}+\frac {3}{28}\right )-4 \ln \left (x +25\right )^{2}+4 \ln \left (x +25\right ) \ln \left (\frac {\RootOf \left (3 \textit {\_Z}^{3}-84 \textit {\_Z}^{2}+1, \mathit {index} =1\right )-x -25}{\RootOf \left (3 \textit {\_Z}^{3}-84 \textit {\_Z}^{2}+1, \mathit {index} =1\right )}\right )+4 \dilog \left (\frac {\RootOf \left (3 \textit {\_Z}^{3}-84 \textit {\_Z}^{2}+1, \mathit {index} =1\right )-x -25}{\RootOf \left (3 \textit {\_Z}^{3}-84 \textit {\_Z}^{2}+1, \mathit {index} =1\right )}\right )+4 \ln \left (x +25\right ) \ln \left (\frac {\RootOf \left (3 \textit {\_Z}^{3}-84 \textit {\_Z}^{2}+1, \mathit {index} =2\right )-x -25}{\RootOf \left (3 \textit {\_Z}^{3}-84 \textit {\_Z}^{2}+1, \mathit {index} =2\right )}\right )+4 \dilog \left (\frac {\RootOf \left (3 \textit {\_Z}^{3}-84 \textit {\_Z}^{2}+1, \mathit {index} =2\right )-x -25}{\RootOf \left (3 \textit {\_Z}^{3}-84 \textit {\_Z}^{2}+1, \mathit {index} =2\right )}\right )+4 \ln \left (x +25\right ) \ln \left (\frac {\RootOf \left (3 \textit {\_Z}^{3}-84 \textit {\_Z}^{2}+1, \mathit {index} =3\right )-x -25}{\RootOf \left (3 \textit {\_Z}^{3}-84 \textit {\_Z}^{2}+1, \mathit {index} =3\right )}\right )+4 \dilog \left (\frac {\RootOf \left (3 \textit {\_Z}^{3}-84 \textit {\_Z}^{2}+1, \mathit {index} =3\right )-x -25}{\RootOf \left (3 \textit {\_Z}^{3}-84 \textit {\_Z}^{2}+1, \mathit {index} =3\right )}\right )\)	\(1016\)
risch	\(\text {Expression too large to display}\)	\(6661\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((6*x+38)*ln((x^3+47*x^2+475*x-1875)/(3*x^3+141*x^2+1425*x-5624))/(3*x^5+207*x^4+4302*x^3+15151*x^2-230603*
x+421800),x,method=_RETURNVERBOSE)

[Out]

ln((x^3+47*x^2+475*x-1875)/(3*x^3+141*x^2+1425*x-5624))^2

________________________________________________________________________________________

maxima [B]  time = 0.35, size = 139, normalized size = 6.04 \begin {gather*} 2 \, {\left (2 \, \log \left (x + 25\right ) + \log \left (x - 3\right )\right )} \log \left (3 \, x^{3} + 141 \, x^{2} + 1425 \, x - 5624\right ) - \log \left (3 \, x^{3} + 141 \, x^{2} + 1425 \, x - 5624\right )^{2} - 4 \, \log \left (x + 25\right )^{2} - 4 \, \log \left (x + 25\right ) \log \left (x - 3\right ) - \log \left (x - 3\right )^{2} - 2 \, {\left (\log \left (3 \, x^{3} + 141 \, x^{2} + 1425 \, x - 5624\right ) - 2 \, \log \left (x + 25\right ) - \log \left (x - 3\right )\right )} \log \left (\frac {x^{3} + 47 \, x^{2} + 475 \, x - 1875}{3 \, x^{3} + 141 \, x^{2} + 1425 \, x - 5624}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((6*x+38)*log((x^3+47*x^2+475*x-1875)/(3*x^3+141*x^2+1425*x-5624))/(3*x^5+207*x^4+4302*x^3+15151*x^2-
230603*x+421800),x, algorithm="maxima")

[Out]

2*(2*log(x + 25) + log(x - 3))*log(3*x^3 + 141*x^2 + 1425*x - 5624) - log(3*x^3 + 141*x^2 + 1425*x - 5624)^2 -
4*log(x + 25)^2 - 4*log(x + 25)*log(x - 3) - log(x - 3)^2 - 2*(log(3*x^3 + 141*x^2 + 1425*x - 5624) - 2*log(x
+ 25) - log(x - 3))*log((x^3 + 47*x^2 + 475*x - 1875)/(3*x^3 + 141*x^2 + 1425*x - 5624))

________________________________________________________________________________________

mupad [B]  time = 1.29, size = 24, normalized size = 1.04 \begin {gather*} {\ln \left (\frac {1}{3}-\frac {1}{3\,\left (3\,x^3+141\,x^2+1425\,x-5624\right )}\right )}^2 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log((475*x + 47*x^2 + x^3 - 1875)/(1425*x + 141*x^2 + 3*x^3 - 5624))*(6*x + 38))/(15151*x^2 - 230603*x +
4302*x^3 + 207*x^4 + 3*x^5 + 421800),x)

[Out]

log(1/3 - 1/(3*(1425*x + 141*x^2 + 3*x^3 - 5624)))^2

________________________________________________________________________________________

sympy [A]  time = 0.20, size = 31, normalized size = 1.35 \begin {gather*} \log {\left (\frac {x^{3} + 47 x^{2} + 475 x - 1875}{3 x^{3} + 141 x^{2} + 1425 x - 5624} \right )}^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((6*x+38)*ln((x**3+47*x**2+475*x-1875)/(3*x**3+141*x**2+1425*x-5624))/(3*x**5+207*x**4+4302*x**3+1515
1*x**2-230603*x+421800),x)

[Out]

log((x**3 + 47*x**2 + 475*x - 1875)/(3*x**3 + 141*x**2 + 1425*x - 5624))**2

________________________________________________________________________________________