Integrand size = 98, antiderivative size = 27 \[ \int \frac {-x^2 \log (3)+\left (2 x+2 x^2\right ) \log ^2(3)+\left (81 x^2+\left (-162 x-324 x^2\right ) \log (3)+\left (81+324 x+324 x^2\right ) \log ^2(3)\right ) \log (5)}{\left (81 x^2+\left (-162 x-324 x^2\right ) \log (3)+\left (81+324 x+324 x^2\right ) \log ^2(3)\right ) \log (5)} \, dx=x+\frac {x^2}{81 \left (1+2 x-\frac {x}{\log (3)}\right ) \log (5)} \] Output:
1/81*x^2/ln(5)/(2*x-x/ln(3)+1)+x
Leaf count is larger than twice the leaf count of optimal. \(65\) vs. \(2(27)=54\).
Time = 0.05 (sec) , antiderivative size = 65, normalized size of antiderivative = 2.41 \[ \int \frac {-x^2 \log (3)+\left (2 x+2 x^2\right ) \log ^2(3)+\left (81 x^2+\left (-162 x-324 x^2\right ) \log (3)+\left (81+324 x+324 x^2\right ) \log ^2(3)\right ) \log (5)}{\left (81 x^2+\left (-162 x-324 x^2\right ) \log (3)+\left (81+324 x+324 x^2\right ) \log ^2(3)\right ) \log (5)} \, dx=\frac {x (\log (3)-81 \log (5)+162 \log (3) \log (5)) (-1+\log (9))+\frac {\log ^2(3) (\log (3)+162 \log (3) \log (5)-81 \log (5) \log (9))}{\log (3)+x (-1+\log (9))}}{81 \log (5) (-1+\log (9))^2} \] Input:
Integrate[(-(x^2*Log[3]) + (2*x + 2*x^2)*Log[3]^2 + (81*x^2 + (-162*x - 32 4*x^2)*Log[3] + (81 + 324*x + 324*x^2)*Log[3]^2)*Log[5])/((81*x^2 + (-162* x - 324*x^2)*Log[3] + (81 + 324*x + 324*x^2)*Log[3]^2)*Log[5]),x]
Output:
(x*(Log[3] - 81*Log[5] + 162*Log[3]*Log[5])*(-1 + Log[9]) + (Log[3]^2*(Log [3] + 162*Log[3]*Log[5] - 81*Log[5]*Log[9]))/(Log[3] + x*(-1 + Log[9])))/( 81*Log[5]*(-1 + Log[9])^2)
Leaf count is larger than twice the leaf count of optimal. \(75\) vs. \(2(27)=54\).
Time = 0.40 (sec) , antiderivative size = 75, normalized size of antiderivative = 2.78, number of steps used = 6, number of rules used = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.061, Rules used = {27, 27, 2007, 2081, 1107, 2009}
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {\log (5) \left (81 x^2+\left (324 x^2+324 x+81\right ) \log ^2(3)+\left (-324 x^2-162 x\right ) \log (3)\right )+\left (2 x^2+2 x\right ) \log ^2(3)+x^2 (-\log (3))}{\log (5) \left (81 x^2+\left (324 x^2+324 x+81\right ) \log ^2(3)+\left (-324 x^2-162 x\right ) \log (3)\right )} \, dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {\int -\frac {\log (3) x^2-81 \left (x^2+\left (4 x^2+4 x+1\right ) \log ^2(3)-2 \left (2 x^2+x\right ) \log (3)\right ) \log (5)-2 \left (x^2+x\right ) \log ^2(3)}{81 \left (x^2+\left (4 x^2+4 x+1\right ) \log ^2(3)-2 \left (2 x^2+x\right ) \log (3)\right )}dx}{\log (5)}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle -\frac {\int \frac {\log (3) x^2-81 \left (x^2+\left (4 x^2+4 x+1\right ) \log ^2(3)-2 \left (2 x^2+x\right ) \log (3)\right ) \log (5)-2 \left (x^2+x\right ) \log ^2(3)}{x^2+\left (4 x^2+4 x+1\right ) \log ^2(3)-2 \left (2 x^2+x\right ) \log (3)}dx}{81 \log (5)}\) |
| \(\Big \downarrow \) 2007 |
| \(\displaystyle -\frac {\int \frac {\log (3) x^2-81 \left (x^2+\left (4 x^2+4 x+1\right ) \log ^2(3)-2 \left (2 x^2+x\right ) \log (3)\right ) \log (5)-2 \left (x^2+x\right ) \log ^2(3)}{((-1+\log (9)) x+\log (3))^2}dx}{81 \log (5)}\) |
| \(\Big \downarrow \) 2081 |
| \(\displaystyle -\frac {\int \frac {(\log (3)-81 \log (5)+162 \log (3) \log (5)) (1-\log (9)) x^2-2 \log (3) (\log (3)-81 \log (5)+162 \log (3) \log (5)) x-81 \log ^2(3) \log (5)}{(\log (3)-x (1-\log (9)))^2}dx}{81 \log (5)}\) |
| \(\Big \downarrow \) 1107 |
| \(\displaystyle -\frac {\int \left (\frac {-81 \log (5)+\log (3) (1+162 \log (5))}{1-\log (9)}+\frac {\log ^2(3) (\log (3)+162 \log (3) \log (5)-81 \log (5) \log (9))}{(-1+\log (9)) ((-1+\log (9)) x+\log (3))^2}\right )dx}{81 \log (5)}\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -\frac {\frac {x (\log (3)-81 \log (5)+162 \log (3) \log (5))}{1-\log (9)}-\frac {\log ^2(3) (\log (3)+162 \log (3) \log (5)-81 \log (5) \log (9))}{(1-\log (9))^2 (\log (3)-x (1-\log (9)))}}{81 \log (5)}\) |
Input:
Int[(-(x^2*Log[3]) + (2*x + 2*x^2)*Log[3]^2 + (81*x^2 + (-162*x - 324*x^2) *Log[3] + (81 + 324*x + 324*x^2)*Log[3]^2)*Log[5])/((81*x^2 + (-162*x - 32 4*x^2)*Log[3] + (81 + 324*x + 324*x^2)*Log[3]^2)*Log[5]),x]
Output:
-1/81*((x*(Log[3] - 81*Log[5] + 162*Log[3]*Log[5]))/(1 - Log[9]) - (Log[3] ^2*(Log[3] + 162*Log[3]*Log[5] - 81*Log[5]*Log[9]))/((Log[3] - x*(1 - Log[ 9]))*(1 - Log[9])^2))/Log[5]
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[((d_.) + (e_.)*(x_))^(m_)*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_.), x_ Symbol] :> Int[ExpandIntegrand[(d + e*x)^m*(a + b*x + c*x^2)^p, x], x] /; F reeQ[{a, b, c, d, e, m}, x] && EqQ[2*c*d - b*e, 0] && IGtQ[p, 0] && !(EqQ[ m, 3] && NeQ[p, 1])
Int[(u_.)*(Px_)^(p_), x_Symbol] :> With[{a = Rt[Coeff[Px, x, 0], Expon[Px, x]], b = Rt[Coeff[Px, x, Expon[Px, x]], Expon[Px, x]]}, Int[u*(a + b*x)^(Ex pon[Px, x]*p), x] /; EqQ[Px, (a + b*x)^Expon[Px, x]]] /; IntegerQ[p] && Pol yQ[Px, x] && GtQ[Expon[Px, x], 1] && NeQ[Coeff[Px, x, 0], 0]
Int[(u_)^(m_.)*(v_)^(p_.), x_Symbol] :> Int[ExpandToSum[u, x]^m*ExpandToSum [v, x]^p, x] /; FreeQ[{m, p}, x] && LinearQ[u, x] && QuadraticQ[v, x] && ! (LinearMatchQ[u, x] && QuadraticMatchQ[v, x])
Time = 0.36 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.56
| method | result | size |
| norman | \(\frac {x \ln \left (3\right )+\frac {\left (162 \ln \left (3\right ) \ln \left (5\right )+\ln \left (3\right )-81 \ln \left (5\right )\right ) x^{2}}{81 \ln \left (5\right )}}{2 x \ln \left (3\right )+\ln \left (3\right )-x}\) | \(42\) |
| gosper | \(\frac {x \left (162 \ln \left (3\right ) \ln \left (5\right ) x +81 \ln \left (3\right ) \ln \left (5\right )+x \ln \left (3\right )-81 x \ln \left (5\right )\right )}{81 \ln \left (5\right ) \left (2 x \ln \left (3\right )+\ln \left (3\right )-x \right )}\) | \(44\) |
| default | \(\frac {\frac {\left (162 \ln \left (3\right ) \ln \left (5\right )+\ln \left (3\right )-81 \ln \left (5\right )\right ) x}{162 \ln \left (3\right )-81}+\frac {\ln \left (3\right )^{3}}{81 \left (2 \ln \left (3\right )-1\right )^{2} \left (2 x \ln \left (3\right )+\ln \left (3\right )-x \right )}}{\ln \left (5\right )}\) | \(58\) |
| parallelrisch | \(\frac {162 \ln \left (3\right )^{2} \ln \left (5\right ) x^{2}+81 \ln \left (3\right )^{2} \ln \left (5\right ) x +x^{2} \ln \left (3\right )^{2}-81 \ln \left (3\right ) \ln \left (5\right ) x^{2}}{81 \ln \left (5\right ) \ln \left (3\right ) \left (2 x \ln \left (3\right )+\ln \left (3\right )-x \right )}\) | \(62\) |
| risch | \(\frac {162 x \ln \left (3\right )}{162 \ln \left (3\right )-81}+\frac {x \ln \left (3\right )}{\ln \left (5\right ) \left (162 \ln \left (3\right )-81\right )}-\frac {81 x}{162 \ln \left (3\right )-81}+\frac {\ln \left (3\right )^{3}}{2 \ln \left (5\right ) \left (2 \ln \left (3\right )-1\right ) \left (162 \ln \left (3\right )-81\right ) \left (x \ln \left (3\right )+\frac {\ln \left (3\right )}{2}-\frac {x}{2}\right )}\) | \(82\) |
| meijerg | \(\frac {81 \left (2 \ln \left (3\right )-1\right )^{2} x}{\left (324 \ln \left (3\right )^{2}-324 \ln \left (3\right )+81\right ) \left (1+\frac {x \left (2 \ln \left (3\right )-1\right )}{\ln \left (3\right )}\right )}+\frac {\left (324 \ln \left (3\right )^{2} \ln \left (5\right )+2 \ln \left (3\right )^{2}-324 \ln \left (3\right ) \ln \left (5\right )-\ln \left (3\right )+81 \ln \left (5\right )\right ) \ln \left (3\right ) \left (\frac {x \left (2 \ln \left (3\right )-1\right ) \left (\frac {3 x \left (2 \ln \left (3\right )-1\right )}{\ln \left (3\right )}+6\right )}{3 \ln \left (3\right ) \left (1+\frac {x \left (2 \ln \left (3\right )-1\right )}{\ln \left (3\right )}\right )}-2 \ln \left (1+\frac {x \left (2 \ln \left (3\right )-1\right )}{\ln \left (3\right )}\right )\right )}{\left (324 \ln \left (3\right )^{2}-324 \ln \left (3\right )+81\right ) \ln \left (5\right ) \left (2 \ln \left (3\right )-1\right )}+\frac {\left (324 \ln \left (3\right )^{2} \ln \left (5\right )+2 \ln \left (3\right )^{2}-162 \ln \left (3\right ) \ln \left (5\right )\right ) \left (-\frac {x \left (2 \ln \left (3\right )-1\right )}{\ln \left (3\right ) \left (1+\frac {x \left (2 \ln \left (3\right )-1\right )}{\ln \left (3\right )}\right )}+\ln \left (1+\frac {x \left (2 \ln \left (3\right )-1\right )}{\ln \left (3\right )}\right )\right )}{\left (324 \ln \left (3\right )^{2}-324 \ln \left (3\right )+81\right ) \ln \left (5\right )}\) | \(248\) |
Input:
int((((324*x^2+324*x+81)*ln(3)^2+(-324*x^2-162*x)*ln(3)+81*x^2)*ln(5)+(2*x ^2+2*x)*ln(3)^2-x^2*ln(3))/((324*x^2+324*x+81)*ln(3)^2+(-324*x^2-162*x)*ln (3)+81*x^2)/ln(5),x,method=_RETURNVERBOSE)
Output:
(x*ln(3)+1/81*(162*ln(3)*ln(5)+ln(3)-81*ln(5))/ln(5)*x^2)/(2*x*ln(3)+ln(3) -x)
Leaf count of result is larger than twice the leaf count of optimal. 123 vs. \(2 (25) = 50\).
Time = 0.07 (sec) , antiderivative size = 123, normalized size of antiderivative = 4.56 \[ \int \frac {-x^2 \log (3)+\left (2 x+2 x^2\right ) \log ^2(3)+\left (81 x^2+\left (-162 x-324 x^2\right ) \log (3)+\left (81+324 x+324 x^2\right ) \log ^2(3)\right ) \log (5)}{\left (81 x^2+\left (-162 x-324 x^2\right ) \log (3)+\left (81+324 x+324 x^2\right ) \log ^2(3)\right ) \log (5)} \, dx=\frac {{\left (4 \, x^{2} + 2 \, x + 1\right )} \log \left (3\right )^{3} + x^{2} \log \left (3\right ) - {\left (4 \, x^{2} + x\right )} \log \left (3\right )^{2} + 81 \, {\left (4 \, {\left (2 \, x^{2} + x\right )} \log \left (3\right )^{3} - 4 \, {\left (3 \, x^{2} + x\right )} \log \left (3\right )^{2} - x^{2} + {\left (6 \, x^{2} + x\right )} \log \left (3\right )\right )} \log \left (5\right )}{81 \, {\left (4 \, {\left (2 \, x + 1\right )} \log \left (3\right )^{3} - 4 \, {\left (3 \, x + 1\right )} \log \left (3\right )^{2} + {\left (6 \, x + 1\right )} \log \left (3\right ) - x\right )} \log \left (5\right )} \] Input:
integrate((((324*x^2+324*x+81)*log(3)^2+(-324*x^2-162*x)*log(3)+81*x^2)*lo g(5)+(2*x^2+2*x)*log(3)^2-x^2*log(3))/((324*x^2+324*x+81)*log(3)^2+(-324*x ^2-162*x)*log(3)+81*x^2)/log(5),x, algorithm="fricas")
Output:
1/81*((4*x^2 + 2*x + 1)*log(3)^3 + x^2*log(3) - (4*x^2 + x)*log(3)^2 + 81* (4*(2*x^2 + x)*log(3)^3 - 4*(3*x^2 + x)*log(3)^2 - x^2 + (6*x^2 + x)*log(3 ))*log(5))/((4*(2*x + 1)*log(3)^3 - 4*(3*x + 1)*log(3)^2 + (6*x + 1)*log(3 ) - x)*log(5))
Leaf count of result is larger than twice the leaf count of optimal. 128 vs. \(2 (19) = 38\).
Time = 0.27 (sec) , antiderivative size = 128, normalized size of antiderivative = 4.74 \[ \int \frac {-x^2 \log (3)+\left (2 x+2 x^2\right ) \log ^2(3)+\left (81 x^2+\left (-162 x-324 x^2\right ) \log (3)+\left (81+324 x+324 x^2\right ) \log ^2(3)\right ) \log (5)}{\left (81 x^2+\left (-162 x-324 x^2\right ) \log (3)+\left (81+324 x+324 x^2\right ) \log ^2(3)\right ) \log (5)} \, dx=x \left (- \frac {81 \log {\left (5 \right )}}{- 81 \log {\left (5 \right )} + 162 \log {\left (3 \right )} \log {\left (5 \right )}} + \frac {\log {\left (3 \right )}}{- 81 \log {\left (5 \right )} + 162 \log {\left (3 \right )} \log {\left (5 \right )}} + \frac {162 \log {\left (3 \right )} \log {\left (5 \right )}}{- 81 \log {\left (5 \right )} + 162 \log {\left (3 \right )} \log {\left (5 \right )}}\right ) + \frac {\log {\left (3 \right )}^{3}}{x \left (- 972 \log {\left (3 \right )}^{2} \log {\left (5 \right )} - 81 \log {\left (5 \right )} + 486 \log {\left (3 \right )} \log {\left (5 \right )} + 648 \log {\left (3 \right )}^{3} \log {\left (5 \right )}\right ) - 324 \log {\left (3 \right )}^{2} \log {\left (5 \right )} + 81 \log {\left (3 \right )} \log {\left (5 \right )} + 324 \log {\left (3 \right )}^{3} \log {\left (5 \right )}} \] Input:
integrate((((324*x**2+324*x+81)*ln(3)**2+(-324*x**2-162*x)*ln(3)+81*x**2)* ln(5)+(2*x**2+2*x)*ln(3)**2-x**2*ln(3))/((324*x**2+324*x+81)*ln(3)**2+(-32 4*x**2-162*x)*ln(3)+81*x**2)/ln(5),x)
Output:
x*(-81*log(5)/(-81*log(5) + 162*log(3)*log(5)) + log(3)/(-81*log(5) + 162* log(3)*log(5)) + 162*log(3)*log(5)/(-81*log(5) + 162*log(3)*log(5))) + log (3)**3/(x*(-972*log(3)**2*log(5) - 81*log(5) + 486*log(3)*log(5) + 648*log (3)**3*log(5)) - 324*log(3)**2*log(5) + 81*log(3)*log(5) + 324*log(3)**3*l og(5))
Leaf count of result is larger than twice the leaf count of optimal. 72 vs. \(2 (25) = 50\).
Time = 0.04 (sec) , antiderivative size = 72, normalized size of antiderivative = 2.67 \[ \int \frac {-x^2 \log (3)+\left (2 x+2 x^2\right ) \log ^2(3)+\left (81 x^2+\left (-162 x-324 x^2\right ) \log (3)+\left (81+324 x+324 x^2\right ) \log ^2(3)\right ) \log (5)}{\left (81 x^2+\left (-162 x-324 x^2\right ) \log (3)+\left (81+324 x+324 x^2\right ) \log ^2(3)\right ) \log (5)} \, dx=\frac {\frac {\log \left (3\right )^{3}}{4 \, \log \left (3\right )^{3} + {\left (8 \, \log \left (3\right )^{3} - 12 \, \log \left (3\right )^{2} + 6 \, \log \left (3\right ) - 1\right )} x - 4 \, \log \left (3\right )^{2} + \log \left (3\right )} + \frac {{\left (81 \, {\left (2 \, \log \left (3\right ) - 1\right )} \log \left (5\right ) + \log \left (3\right )\right )} x}{2 \, \log \left (3\right ) - 1}}{81 \, \log \left (5\right )} \] Input:
integrate((((324*x^2+324*x+81)*log(3)^2+(-324*x^2-162*x)*log(3)+81*x^2)*lo g(5)+(2*x^2+2*x)*log(3)^2-x^2*log(3))/((324*x^2+324*x+81)*log(3)^2+(-324*x ^2-162*x)*log(3)+81*x^2)/log(5),x, algorithm="maxima")
Output:
1/81*(log(3)^3/(4*log(3)^3 + (8*log(3)^3 - 12*log(3)^2 + 6*log(3) - 1)*x - 4*log(3)^2 + log(3)) + (81*(2*log(3) - 1)*log(5) + log(3))*x/(2*log(3) - 1))/log(5)
Leaf count of result is larger than twice the leaf count of optimal. 88 vs. \(2 (25) = 50\).
Time = 0.12 (sec) , antiderivative size = 88, normalized size of antiderivative = 3.26 \[ \int \frac {-x^2 \log (3)+\left (2 x+2 x^2\right ) \log ^2(3)+\left (81 x^2+\left (-162 x-324 x^2\right ) \log (3)+\left (81+324 x+324 x^2\right ) \log ^2(3)\right ) \log (5)}{\left (81 x^2+\left (-162 x-324 x^2\right ) \log (3)+\left (81+324 x+324 x^2\right ) \log ^2(3)\right ) \log (5)} \, dx=\frac {\frac {\log \left (3\right )^{3}}{{\left (2 \, x \log \left (3\right ) - x + \log \left (3\right )\right )} {\left (4 \, \log \left (3\right )^{2} - 4 \, \log \left (3\right ) + 1\right )}} + \frac {324 \, x \log \left (5\right ) \log \left (3\right )^{2} - 324 \, x \log \left (5\right ) \log \left (3\right ) + 2 \, x \log \left (3\right )^{2} + 81 \, x \log \left (5\right ) - x \log \left (3\right )}{4 \, \log \left (3\right )^{2} - 4 \, \log \left (3\right ) + 1}}{81 \, \log \left (5\right )} \] Input:
integrate((((324*x^2+324*x+81)*log(3)^2+(-324*x^2-162*x)*log(3)+81*x^2)*lo g(5)+(2*x^2+2*x)*log(3)^2-x^2*log(3))/((324*x^2+324*x+81)*log(3)^2+(-324*x ^2-162*x)*log(3)+81*x^2)/log(5),x, algorithm="giac")
Output:
1/81*(log(3)^3/((2*x*log(3) - x + log(3))*(4*log(3)^2 - 4*log(3) + 1)) + ( 324*x*log(5)*log(3)^2 - 324*x*log(5)*log(3) + 2*x*log(3)^2 + 81*x*log(5) - x*log(3))/(4*log(3)^2 - 4*log(3) + 1))/log(5)
Time = 0.28 (sec) , antiderivative size = 82, normalized size of antiderivative = 3.04 \[ \int \frac {-x^2 \log (3)+\left (2 x+2 x^2\right ) \log ^2(3)+\left (81 x^2+\left (-162 x-324 x^2\right ) \log (3)+\left (81+324 x+324 x^2\right ) \log ^2(3)\right ) \log (5)}{\left (81 x^2+\left (-162 x-324 x^2\right ) \log (3)+\left (81+324 x+324 x^2\right ) \log ^2(3)\right ) \log (5)} \, dx=\frac {{\ln \left (3\right )}^3}{\left (\ln \left (9\right )-1\right )\,\left (x\,\left (81\,\ln \left (5\right )-162\,\ln \left (5\right )\,\ln \left (9\right )+81\,\ln \left (5\right )\,{\ln \left (9\right )}^2\right )-81\,\ln \left (3\right )\,\ln \left (5\right )+81\,\ln \left (3\right )\,\ln \left (5\right )\,\ln \left (9\right )\right )}+\frac {x\,\left (2\,\ln \left (3\right )-1\right )\,\left (\ln \left (3\right )-81\,\ln \left (5\right )+162\,\ln \left (3\right )\,\ln \left (5\right )\right )}{81\,\ln \left (5\right )\,{\left (\ln \left (9\right )-1\right )}^2} \] Input:
int((log(5)*(log(3)^2*(324*x + 324*x^2 + 81) - log(3)*(162*x + 324*x^2) + 81*x^2) + log(3)^2*(2*x + 2*x^2) - x^2*log(3))/(log(5)*(log(3)^2*(324*x + 324*x^2 + 81) - log(3)*(162*x + 324*x^2) + 81*x^2)),x)
Output:
log(3)^3/((log(9) - 1)*(x*(81*log(5) - 162*log(5)*log(9) + 81*log(5)*log(9 )^2) - 81*log(3)*log(5) + 81*log(3)*log(5)*log(9))) + (x*(2*log(3) - 1)*(l og(3) - 81*log(5) + 162*log(3)*log(5)))/(81*log(5)*(log(9) - 1)^2)
Time = 0.23 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.59 \[ \int \frac {-x^2 \log (3)+\left (2 x+2 x^2\right ) \log ^2(3)+\left (81 x^2+\left (-162 x-324 x^2\right ) \log (3)+\left (81+324 x+324 x^2\right ) \log ^2(3)\right ) \log (5)}{\left (81 x^2+\left (-162 x-324 x^2\right ) \log (3)+\left (81+324 x+324 x^2\right ) \log ^2(3)\right ) \log (5)} \, dx=\frac {x \left (162 \,\mathrm {log}\left (5\right ) \mathrm {log}\left (3\right ) x +81 \,\mathrm {log}\left (5\right ) \mathrm {log}\left (3\right )-81 \,\mathrm {log}\left (5\right ) x +\mathrm {log}\left (3\right ) x \right )}{81 \,\mathrm {log}\left (5\right ) \left (2 \,\mathrm {log}\left (3\right ) x +\mathrm {log}\left (3\right )-x \right )} \] Input:
int((((324*x^2+324*x+81)*log(3)^2+(-324*x^2-162*x)*log(3)+81*x^2)*log(5)+( 2*x^2+2*x)*log(3)^2-x^2*log(3))/((324*x^2+324*x+81)*log(3)^2+(-324*x^2-162 *x)*log(3)+81*x^2)/log(5),x)
Output:
(x*(162*log(5)*log(3)*x + 81*log(5)*log(3) - 81*log(5)*x + log(3)*x))/(81* log(5)*(2*log(3)*x + log(3) - x))