Integrand size = 102, antiderivative size = 33 \[ \int \frac {9+55 x^2-42 x^3-9 x^4-8 x^5-5 x^6+\left (-36 x^4+16 x^5+20 x^6+24 x^7\right ) \log (5)+\left (24 x^5-10 x^6-12 x^7-42 x^8\right ) \log ^2(5)+32 x^9 \log ^3(5)-9 x^{10} \log ^4(5)}{25 x^2} \, dx=x \left (2-x-\frac {1}{25} \left (1-\frac {3}{x}+x+\left (-x+x^2 \log (5)\right )^2\right )^2\right ) \] Output:
x*(2-x-1/5*(x+1+(x^2*ln(5)-x)^2-3/x)*(1/5*x+1/5+1/5*(x^2*ln(5)-x)^2-3/5/x) )
Leaf count is larger than twice the leaf count of optimal. \(97\) vs. \(2(33)=66\).
Time = 0.03 (sec) , antiderivative size = 97, normalized size of antiderivative = 2.94 \[ \int \frac {9+55 x^2-42 x^3-9 x^4-8 x^5-5 x^6+\left (-36 x^4+16 x^5+20 x^6+24 x^7\right ) \log (5)+\left (24 x^5-10 x^6-12 x^7-42 x^8\right ) \log ^2(5)+32 x^9 \log ^3(5)-9 x^{10} \log ^4(5)}{25 x^2} \, dx=\frac {1}{25} \left (-\frac {9}{x}+55 x-21 x^2-2 x^6 (-2+\log (5)) \log (5)-6 x^7 \log ^2(5)+4 x^8 \log ^3(5)-x^9 \log ^4(5)-x^5 \left (1-4 \log (5)+2 \log ^2(5)\right )+2 x^4 \left (-1+3 \log ^2(5)+\log (25)\right )-3 x^3 (1+\log (625))\right ) \] Input:
Integrate[(9 + 55*x^2 - 42*x^3 - 9*x^4 - 8*x^5 - 5*x^6 + (-36*x^4 + 16*x^5 + 20*x^6 + 24*x^7)*Log[5] + (24*x^5 - 10*x^6 - 12*x^7 - 42*x^8)*Log[5]^2 + 32*x^9*Log[5]^3 - 9*x^10*Log[5]^4)/(25*x^2),x]
Output:
(-9/x + 55*x - 21*x^2 - 2*x^6*(-2 + Log[5])*Log[5] - 6*x^7*Log[5]^2 + 4*x^ 8*Log[5]^3 - x^9*Log[5]^4 - x^5*(1 - 4*Log[5] + 2*Log[5]^2) + 2*x^4*(-1 + 3*Log[5]^2 + Log[25]) - 3*x^3*(1 + Log[625]))/25
Leaf count is larger than twice the leaf count of optimal. \(101\) vs. \(2(33)=66\).
Time = 0.35 (sec) , antiderivative size = 101, normalized size of antiderivative = 3.06, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.029, Rules used = {27, 2010, 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.
| \(\displaystyle \int \frac {-9 x^{10} \log ^4(5)+32 x^9 \log ^3(5)-5 x^6-8 x^5-9 x^4-42 x^3+55 x^2+\left (-42 x^8-12 x^7-10 x^6+24 x^5\right ) \log ^2(5)+\left (24 x^7+20 x^6+16 x^5-36 x^4\right ) \log (5)+9}{25 x^2} \, dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{25} \int \frac {-9 \log ^4(5) x^{10}+32 \log ^3(5) x^9-5 x^6-8 x^5-9 x^4-42 x^3+55 x^2+2 \left (-21 x^8-6 x^7-5 x^6+12 x^5\right ) \log ^2(5)-4 \left (-6 x^7-5 x^6-4 x^5+9 x^4\right ) \log (5)+9}{x^2}dx\) |
| \(\Big \downarrow \) 2010 |
| \(\displaystyle \frac {1}{25} \int \left (-9 \log ^4(5) x^8+32 \log ^3(5) x^7-42 \log ^2(5) x^6-12 (-2+\log (5)) \log (5) x^5-5 \left (1-4 \log (5)+2 \log ^2(5)\right ) x^4+8 \left (-1+3 \log ^2(5)+\log (25)\right ) x^3-9 (1+\log (625)) x^2-42 x+55+\frac {9}{x^2}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {1}{25} \left (x^9 \left (-\log ^4(5)\right )+4 x^8 \log ^3(5)-6 x^7 \log ^2(5)+2 x^6 (2-\log (5)) \log (5)-x^5 \left (1+2 \log ^2(5)-\log (625)\right )-2 x^4 \left (1-3 \log ^2(5)-\log (25)\right )-3 x^3 (1+\log (625))-21 x^2+55 x-\frac {9}{x}\right )\) |
Input:
Int[(9 + 55*x^2 - 42*x^3 - 9*x^4 - 8*x^5 - 5*x^6 + (-36*x^4 + 16*x^5 + 20* x^6 + 24*x^7)*Log[5] + (24*x^5 - 10*x^6 - 12*x^7 - 42*x^8)*Log[5]^2 + 32*x ^9*Log[5]^3 - 9*x^10*Log[5]^4)/(25*x^2),x]
Output:
(-9/x + 55*x - 21*x^2 + 2*x^6*(2 - Log[5])*Log[5] - 6*x^7*Log[5]^2 + 4*x^8 *Log[5]^3 - x^9*Log[5]^4 - 2*x^4*(1 - 3*Log[5]^2 - Log[25]) - x^5*(1 + 2*L og[5]^2 - Log[625]) - 3*x^3*(1 + Log[625]))/25
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[(u_)*((c_.)*(x_))^(m_.), x_Symbol] :> Int[ExpandIntegrand[(c*x)^m*u, x] , x] /; FreeQ[{c, m}, x] && SumQ[u] && !LinearQ[u, x] && !MatchQ[u, (a_) + (b_.)*(v_) /; FreeQ[{a, b}, x] && InverseFunctionQ[v]]
Time = 0.13 (sec) , antiderivative size = 101, normalized size of antiderivative = 3.06
| method | result | size |
| norman | \(\frac {-\frac {9}{25}+\left (-\frac {2 \ln \left (5\right )^{2}}{25}+\frac {4 \ln \left (5\right )}{25}\right ) x^{7}+\left (-\frac {12 \ln \left (5\right )}{25}-\frac {3}{25}\right ) x^{4}+\left (-\frac {2 \ln \left (5\right )^{2}}{25}+\frac {4 \ln \left (5\right )}{25}-\frac {1}{25}\right ) x^{6}+\left (\frac {6 \ln \left (5\right )^{2}}{25}+\frac {4 \ln \left (5\right )}{25}-\frac {2}{25}\right ) x^{5}+\frac {11 x^{2}}{5}-\frac {21 x^{3}}{25}+\frac {4 x^{9} \ln \left (5\right )^{3}}{25}-\frac {x^{10} \ln \left (5\right )^{4}}{25}-\frac {6 \ln \left (5\right )^{2} x^{8}}{25}}{x}\) | \(101\) |
| gosper | \(-\frac {x^{10} \ln \left (5\right )^{4}-4 x^{9} \ln \left (5\right )^{3}+6 \ln \left (5\right )^{2} x^{8}+2 x^{7} \ln \left (5\right )^{2}+2 x^{6} \ln \left (5\right )^{2}-4 x^{7} \ln \left (5\right )-6 x^{5} \ln \left (5\right )^{2}-4 x^{6} \ln \left (5\right )-4 x^{5} \ln \left (5\right )+x^{6}+12 x^{4} \ln \left (5\right )+2 x^{5}+3 x^{4}+21 x^{3}-55 x^{2}+9}{25 x}\) | \(112\) |
| default | \(-\frac {\ln \left (5\right )^{4} x^{9}}{25}+\frac {4 \ln \left (5\right )^{3} x^{8}}{25}-\frac {6 x^{7} \ln \left (5\right )^{2}}{25}-\frac {2 x^{6} \ln \left (5\right )^{2}}{25}-\frac {2 x^{5} \ln \left (5\right )^{2}}{25}+\frac {4 x^{6} \ln \left (5\right )}{25}+\frac {6 x^{4} \ln \left (5\right )^{2}}{25}+\frac {4 x^{5} \ln \left (5\right )}{25}+\frac {4 x^{4} \ln \left (5\right )}{25}-\frac {x^{5}}{25}-\frac {12 x^{3} \ln \left (5\right )}{25}-\frac {2 x^{4}}{25}-\frac {3 x^{3}}{25}-\frac {21 x^{2}}{25}+\frac {11 x}{5}-\frac {9}{25 x}\) | \(112\) |
| risch | \(-\frac {\ln \left (5\right )^{4} x^{9}}{25}+\frac {4 \ln \left (5\right )^{3} x^{8}}{25}-\frac {6 x^{7} \ln \left (5\right )^{2}}{25}-\frac {2 x^{6} \ln \left (5\right )^{2}}{25}-\frac {2 x^{5} \ln \left (5\right )^{2}}{25}+\frac {4 x^{6} \ln \left (5\right )}{25}+\frac {6 x^{4} \ln \left (5\right )^{2}}{25}+\frac {4 x^{5} \ln \left (5\right )}{25}+\frac {4 x^{4} \ln \left (5\right )}{25}-\frac {x^{5}}{25}-\frac {12 x^{3} \ln \left (5\right )}{25}-\frac {2 x^{4}}{25}-\frac {3 x^{3}}{25}-\frac {21 x^{2}}{25}+\frac {11 x}{5}-\frac {9}{25 x}\) | \(112\) |
| parallelrisch | \(-\frac {x^{10} \ln \left (5\right )^{4}-4 x^{9} \ln \left (5\right )^{3}+6 \ln \left (5\right )^{2} x^{8}+2 x^{7} \ln \left (5\right )^{2}+2 x^{6} \ln \left (5\right )^{2}-4 x^{7} \ln \left (5\right )-6 x^{5} \ln \left (5\right )^{2}-4 x^{6} \ln \left (5\right )-4 x^{5} \ln \left (5\right )+x^{6}+12 x^{4} \ln \left (5\right )+2 x^{5}+3 x^{4}+21 x^{3}-55 x^{2}+9}{25 x}\) | \(112\) |
| orering | \(\frac {\left (x^{10} \ln \left (5\right )^{4}-4 x^{9} \ln \left (5\right )^{3}+6 \ln \left (5\right )^{2} x^{8}+2 x^{7} \ln \left (5\right )^{2}+2 x^{6} \ln \left (5\right )^{2}-4 x^{7} \ln \left (5\right )-6 x^{5} \ln \left (5\right )^{2}-4 x^{6} \ln \left (5\right )-4 x^{5} \ln \left (5\right )+x^{6}+12 x^{4} \ln \left (5\right )+2 x^{5}+3 x^{4}+21 x^{3}-55 x^{2}+9\right ) \left (-9 x^{10} \ln \left (5\right )^{4}+32 x^{9} \ln \left (5\right )^{3}+\left (-42 x^{8}-12 x^{7}-10 x^{6}+24 x^{5}\right ) \ln \left (5\right )^{2}+\left (24 x^{7}+20 x^{6}+16 x^{5}-36 x^{4}\right ) \ln \left (5\right )-5 x^{6}-8 x^{5}-9 x^{4}-42 x^{3}+55 x^{2}+9\right )}{25 x \left (9 x^{10} \ln \left (5\right )^{4}-32 x^{9} \ln \left (5\right )^{3}+42 \ln \left (5\right )^{2} x^{8}+12 x^{7} \ln \left (5\right )^{2}+10 x^{6} \ln \left (5\right )^{2}-24 x^{7} \ln \left (5\right )-24 x^{5} \ln \left (5\right )^{2}-20 x^{6} \ln \left (5\right )-16 x^{5} \ln \left (5\right )+5 x^{6}+36 x^{4} \ln \left (5\right )+8 x^{5}+9 x^{4}+42 x^{3}-55 x^{2}-9\right )}\) | \(318\) |
Input:
int(1/25*(-9*x^10*ln(5)^4+32*x^9*ln(5)^3+(-42*x^8-12*x^7-10*x^6+24*x^5)*ln (5)^2+(24*x^7+20*x^6+16*x^5-36*x^4)*ln(5)-5*x^6-8*x^5-9*x^4-42*x^3+55*x^2+ 9)/x^2,x,method=_RETURNVERBOSE)
Output:
(-9/25+(-2/25*ln(5)^2+4/25*ln(5))*x^7+(-12/25*ln(5)-3/25)*x^4+(-2/25*ln(5) ^2+4/25*ln(5)-1/25)*x^6+(6/25*ln(5)^2+4/25*ln(5)-2/25)*x^5+11/5*x^2-21/25* x^3+4/25*x^9*ln(5)^3-1/25*x^10*ln(5)^4-6/25*ln(5)^2*x^8)/x
Leaf count of result is larger than twice the leaf count of optimal. 89 vs. \(2 (30) = 60\).
Time = 0.07 (sec) , antiderivative size = 89, normalized size of antiderivative = 2.70 \[ \int \frac {9+55 x^2-42 x^3-9 x^4-8 x^5-5 x^6+\left (-36 x^4+16 x^5+20 x^6+24 x^7\right ) \log (5)+\left (24 x^5-10 x^6-12 x^7-42 x^8\right ) \log ^2(5)+32 x^9 \log ^3(5)-9 x^{10} \log ^4(5)}{25 x^2} \, dx=-\frac {x^{10} \log \left (5\right )^{4} - 4 \, x^{9} \log \left (5\right )^{3} + x^{6} + 2 \, x^{5} + 3 \, x^{4} + 21 \, x^{3} + 2 \, {\left (3 \, x^{8} + x^{7} + x^{6} - 3 \, x^{5}\right )} \log \left (5\right )^{2} - 55 \, x^{2} - 4 \, {\left (x^{7} + x^{6} + x^{5} - 3 \, x^{4}\right )} \log \left (5\right ) + 9}{25 \, x} \] Input:
integrate(1/25*(-9*x^10*log(5)^4+32*x^9*log(5)^3+(-42*x^8-12*x^7-10*x^6+24 *x^5)*log(5)^2+(24*x^7+20*x^6+16*x^5-36*x^4)*log(5)-5*x^6-8*x^5-9*x^4-42*x ^3+55*x^2+9)/x^2,x, algorithm="fricas")
Output:
-1/25*(x^10*log(5)^4 - 4*x^9*log(5)^3 + x^6 + 2*x^5 + 3*x^4 + 21*x^3 + 2*( 3*x^8 + x^7 + x^6 - 3*x^5)*log(5)^2 - 55*x^2 - 4*(x^7 + x^6 + x^5 - 3*x^4) *log(5) + 9)/x
Leaf count of result is larger than twice the leaf count of optimal. 116 vs. \(2 (29) = 58\).
Time = 0.09 (sec) , antiderivative size = 116, normalized size of antiderivative = 3.52 \[ \int \frac {9+55 x^2-42 x^3-9 x^4-8 x^5-5 x^6+\left (-36 x^4+16 x^5+20 x^6+24 x^7\right ) \log (5)+\left (24 x^5-10 x^6-12 x^7-42 x^8\right ) \log ^2(5)+32 x^9 \log ^3(5)-9 x^{10} \log ^4(5)}{25 x^2} \, dx=- \frac {x^{9} \log {\left (5 \right )}^{4}}{25} + \frac {4 x^{8} \log {\left (5 \right )}^{3}}{25} - \frac {6 x^{7} \log {\left (5 \right )}^{2}}{25} - \frac {x^{6} \left (- 4 \log {\left (5 \right )} + 2 \log {\left (5 \right )}^{2}\right )}{25} - \frac {x^{5} \left (- 4 \log {\left (5 \right )} + 1 + 2 \log {\left (5 \right )}^{2}\right )}{25} - \frac {x^{4} \left (- 6 \log {\left (5 \right )}^{2} - 4 \log {\left (5 \right )} + 2\right )}{25} - \frac {x^{3} \cdot \left (3 + 12 \log {\left (5 \right )}\right )}{25} - \frac {21 x^{2}}{25} + \frac {11 x}{5} - \frac {9}{25 x} \] Input:
integrate(1/25*(-9*x**10*ln(5)**4+32*x**9*ln(5)**3+(-42*x**8-12*x**7-10*x* *6+24*x**5)*ln(5)**2+(24*x**7+20*x**6+16*x**5-36*x**4)*ln(5)-5*x**6-8*x**5 -9*x**4-42*x**3+55*x**2+9)/x**2,x)
Output:
-x**9*log(5)**4/25 + 4*x**8*log(5)**3/25 - 6*x**7*log(5)**2/25 - x**6*(-4* log(5) + 2*log(5)**2)/25 - x**5*(-4*log(5) + 1 + 2*log(5)**2)/25 - x**4*(- 6*log(5)**2 - 4*log(5) + 2)/25 - x**3*(3 + 12*log(5))/25 - 21*x**2/25 + 11 *x/5 - 9/(25*x)
Leaf count of result is larger than twice the leaf count of optimal. 100 vs. \(2 (30) = 60\).
Time = 0.03 (sec) , antiderivative size = 100, normalized size of antiderivative = 3.03 \[ \int \frac {9+55 x^2-42 x^3-9 x^4-8 x^5-5 x^6+\left (-36 x^4+16 x^5+20 x^6+24 x^7\right ) \log (5)+\left (24 x^5-10 x^6-12 x^7-42 x^8\right ) \log ^2(5)+32 x^9 \log ^3(5)-9 x^{10} \log ^4(5)}{25 x^2} \, dx=-\frac {1}{25} \, x^{9} \log \left (5\right )^{4} + \frac {4}{25} \, x^{8} \log \left (5\right )^{3} - \frac {6}{25} \, x^{7} \log \left (5\right )^{2} - \frac {2}{25} \, {\left (\log \left (5\right )^{2} - 2 \, \log \left (5\right )\right )} x^{6} - \frac {1}{25} \, {\left (2 \, \log \left (5\right )^{2} - 4 \, \log \left (5\right ) + 1\right )} x^{5} + \frac {2}{25} \, {\left (3 \, \log \left (5\right )^{2} + 2 \, \log \left (5\right ) - 1\right )} x^{4} - \frac {3}{25} \, x^{3} {\left (4 \, \log \left (5\right ) + 1\right )} - \frac {21}{25} \, x^{2} + \frac {11}{5} \, x - \frac {9}{25 \, x} \] Input:
integrate(1/25*(-9*x^10*log(5)^4+32*x^9*log(5)^3+(-42*x^8-12*x^7-10*x^6+24 *x^5)*log(5)^2+(24*x^7+20*x^6+16*x^5-36*x^4)*log(5)-5*x^6-8*x^5-9*x^4-42*x ^3+55*x^2+9)/x^2,x, algorithm="maxima")
Output:
-1/25*x^9*log(5)^4 + 4/25*x^8*log(5)^3 - 6/25*x^7*log(5)^2 - 2/25*(log(5)^ 2 - 2*log(5))*x^6 - 1/25*(2*log(5)^2 - 4*log(5) + 1)*x^5 + 2/25*(3*log(5)^ 2 + 2*log(5) - 1)*x^4 - 3/25*x^3*(4*log(5) + 1) - 21/25*x^2 + 11/5*x - 9/2 5/x
Leaf count of result is larger than twice the leaf count of optimal. 111 vs. \(2 (30) = 60\).
Time = 0.11 (sec) , antiderivative size = 111, normalized size of antiderivative = 3.36 \[ \int \frac {9+55 x^2-42 x^3-9 x^4-8 x^5-5 x^6+\left (-36 x^4+16 x^5+20 x^6+24 x^7\right ) \log (5)+\left (24 x^5-10 x^6-12 x^7-42 x^8\right ) \log ^2(5)+32 x^9 \log ^3(5)-9 x^{10} \log ^4(5)}{25 x^2} \, dx=-\frac {1}{25} \, x^{9} \log \left (5\right )^{4} + \frac {4}{25} \, x^{8} \log \left (5\right )^{3} - \frac {6}{25} \, x^{7} \log \left (5\right )^{2} - \frac {2}{25} \, x^{6} \log \left (5\right )^{2} + \frac {4}{25} \, x^{6} \log \left (5\right ) - \frac {2}{25} \, x^{5} \log \left (5\right )^{2} + \frac {4}{25} \, x^{5} \log \left (5\right ) + \frac {6}{25} \, x^{4} \log \left (5\right )^{2} - \frac {1}{25} \, x^{5} + \frac {4}{25} \, x^{4} \log \left (5\right ) - \frac {2}{25} \, x^{4} - \frac {12}{25} \, x^{3} \log \left (5\right ) - \frac {3}{25} \, x^{3} - \frac {21}{25} \, x^{2} + \frac {11}{5} \, x - \frac {9}{25 \, x} \] Input:
integrate(1/25*(-9*x^10*log(5)^4+32*x^9*log(5)^3+(-42*x^8-12*x^7-10*x^6+24 *x^5)*log(5)^2+(24*x^7+20*x^6+16*x^5-36*x^4)*log(5)-5*x^6-8*x^5-9*x^4-42*x ^3+55*x^2+9)/x^2,x, algorithm="giac")
Output:
-1/25*x^9*log(5)^4 + 4/25*x^8*log(5)^3 - 6/25*x^7*log(5)^2 - 2/25*x^6*log( 5)^2 + 4/25*x^6*log(5) - 2/25*x^5*log(5)^2 + 4/25*x^5*log(5) + 6/25*x^4*lo g(5)^2 - 1/25*x^5 + 4/25*x^4*log(5) - 2/25*x^4 - 12/25*x^3*log(5) - 3/25*x ^3 - 21/25*x^2 + 11/5*x - 9/25/x
Time = 2.35 (sec) , antiderivative size = 100, normalized size of antiderivative = 3.03 \[ \int \frac {9+55 x^2-42 x^3-9 x^4-8 x^5-5 x^6+\left (-36 x^4+16 x^5+20 x^6+24 x^7\right ) \log (5)+\left (24 x^5-10 x^6-12 x^7-42 x^8\right ) \log ^2(5)+32 x^9 \log ^3(5)-9 x^{10} \log ^4(5)}{25 x^2} \, dx=\frac {11\,x}{5}-\frac {6\,x^7\,{\ln \left (5\right )}^2}{25}+\frac {4\,x^8\,{\ln \left (5\right )}^3}{25}-\frac {x^9\,{\ln \left (5\right )}^4}{25}-x^3\,\left (\frac {12\,\ln \left (5\right )}{25}+\frac {3}{25}\right )+x^6\,\left (\frac {4\,\ln \left (5\right )}{25}-\frac {2\,{\ln \left (5\right )}^2}{25}\right )-x^5\,\left (\frac {2\,{\ln \left (5\right )}^2}{25}-\frac {4\,\ln \left (5\right )}{25}+\frac {1}{25}\right )+x^4\,\left (\frac {4\,\ln \left (5\right )}{25}+\frac {6\,{\ln \left (5\right )}^2}{25}-\frac {2}{25}\right )-\frac {9}{25\,x}-\frac {21\,x^2}{25} \] Input:
int(-((9*x^10*log(5)^4)/25 - (32*x^9*log(5)^3)/25 - (log(5)*(16*x^5 - 36*x ^4 + 20*x^6 + 24*x^7))/25 + (log(5)^2*(10*x^6 - 24*x^5 + 12*x^7 + 42*x^8)) /25 - (11*x^2)/5 + (42*x^3)/25 + (9*x^4)/25 + (8*x^5)/25 + x^6/5 - 9/25)/x ^2,x)
Output:
(11*x)/5 - (6*x^7*log(5)^2)/25 + (4*x^8*log(5)^3)/25 - (x^9*log(5)^4)/25 - x^3*((12*log(5))/25 + 3/25) + x^6*((4*log(5))/25 - (2*log(5)^2)/25) - x^5 *((2*log(5)^2)/25 - (4*log(5))/25 + 1/25) + x^4*((4*log(5))/25 + (6*log(5) ^2)/25 - 2/25) - 9/(25*x) - (21*x^2)/25
Time = 0.26 (sec) , antiderivative size = 114, normalized size of antiderivative = 3.45 \[ \int \frac {9+55 x^2-42 x^3-9 x^4-8 x^5-5 x^6+\left (-36 x^4+16 x^5+20 x^6+24 x^7\right ) \log (5)+\left (24 x^5-10 x^6-12 x^7-42 x^8\right ) \log ^2(5)+32 x^9 \log ^3(5)-9 x^{10} \log ^4(5)}{25 x^2} \, dx=\frac {-\mathrm {log}\left (5\right )^{4} x^{10}+4 \mathrm {log}\left (5\right )^{3} x^{9}-6 \mathrm {log}\left (5\right )^{2} x^{8}-2 \mathrm {log}\left (5\right )^{2} x^{7}-2 \mathrm {log}\left (5\right )^{2} x^{6}+6 \mathrm {log}\left (5\right )^{2} x^{5}+4 \,\mathrm {log}\left (5\right ) x^{7}+4 \,\mathrm {log}\left (5\right ) x^{6}+4 \,\mathrm {log}\left (5\right ) x^{5}-12 \,\mathrm {log}\left (5\right ) x^{4}-x^{6}-2 x^{5}-3 x^{4}-21 x^{3}+55 x^{2}-9}{25 x} \] Input:
int(1/25*(-9*x^10*log(5)^4+32*x^9*log(5)^3+(-42*x^8-12*x^7-10*x^6+24*x^5)* log(5)^2+(24*x^7+20*x^6+16*x^5-36*x^4)*log(5)-5*x^6-8*x^5-9*x^4-42*x^3+55* x^2+9)/x^2,x)
Output:
( - log(5)**4*x**10 + 4*log(5)**3*x**9 - 6*log(5)**2*x**8 - 2*log(5)**2*x* *7 - 2*log(5)**2*x**6 + 6*log(5)**2*x**5 + 4*log(5)*x**7 + 4*log(5)*x**6 + 4*log(5)*x**5 - 12*log(5)*x**4 - x**6 - 2*x**5 - 3*x**4 - 21*x**3 + 55*x* *2 - 9)/(25*x)