Integrand size = 259, antiderivative size = 31 \[ \int \frac {-600 x^7-900 x^8-300 x^9+150 x^{10}+e^{\log ^2(x)} \left (-750 x^4-2700 x^5-3600 x^6-1050 x^7+1350 x^8+750 x^9-300 x^{10}+\left (-300 x^4-1200 x^5-1800 x^6-600 x^7+900 x^8+600 x^9-300 x^{10}\right ) \log (x)\right )+e^{2 \log ^2(x)} \left (-150 x-900 x^2-2250 x^3-2550 x^4-450 x^5+1800 x^6+1200 x^7-450 x^8-450 x^9+150 x^{10}+\left (-300 x-1800 x^2-4500 x^3-5100 x^4-900 x^5+3600 x^6+2400 x^7-900 x^8-900 x^9+300 x^{10}\right ) \log (x)\right )}{-1-6 x-15 x^2-17 x^3-3 x^4+12 x^5+8 x^6-3 x^7-3 x^8+x^9} \, dx=75 x^2 \left (e^{\log ^2(x)}-\frac {x}{x-\frac {(1+x)^2}{x^2}}\right )^2 \] Output:
75*(exp(ln(x)^2)-x/(x-(1+x)^2/x^2))^2*x^2
Leaf count is larger than twice the leaf count of optimal. \(100\) vs. \(2(31)=62\).
Time = 0.13 (sec) , antiderivative size = 100, normalized size of antiderivative = 3.23 \[ \int \frac {-600 x^7-900 x^8-300 x^9+150 x^{10}+e^{\log ^2(x)} \left (-750 x^4-2700 x^5-3600 x^6-1050 x^7+1350 x^8+750 x^9-300 x^{10}+\left (-300 x^4-1200 x^5-1800 x^6-600 x^7+900 x^8+600 x^9-300 x^{10}\right ) \log (x)\right )+e^{2 \log ^2(x)} \left (-150 x-900 x^2-2250 x^3-2550 x^4-450 x^5+1800 x^6+1200 x^7-450 x^8-450 x^9+150 x^{10}+\left (-300 x-1800 x^2-4500 x^3-5100 x^4-900 x^5+3600 x^6+2400 x^7-900 x^8-900 x^9+300 x^{10}\right ) \log (x)\right )}{-1-6 x-15 x^2-17 x^3-3 x^4+12 x^5+8 x^6-3 x^7-3 x^8+x^9} \, dx=75 \left (2 x+x^2+e^{2 \log ^2(x)} x^2+\frac {28+69 x+60 x^2}{\left (1+2 x+x^2-x^3\right )^2}+\frac {2 e^{\log ^2(x)} x^5}{1+2 x+x^2-x^3}-\frac {35+29 x+18 x^2}{1+2 x+x^2-x^3}\right ) \] Input:
Integrate[(-600*x^7 - 900*x^8 - 300*x^9 + 150*x^10 + E^Log[x]^2*(-750*x^4 - 2700*x^5 - 3600*x^6 - 1050*x^7 + 1350*x^8 + 750*x^9 - 300*x^10 + (-300*x ^4 - 1200*x^5 - 1800*x^6 - 600*x^7 + 900*x^8 + 600*x^9 - 300*x^10)*Log[x]) + E^(2*Log[x]^2)*(-150*x - 900*x^2 - 2250*x^3 - 2550*x^4 - 450*x^5 + 1800 *x^6 + 1200*x^7 - 450*x^8 - 450*x^9 + 150*x^10 + (-300*x - 1800*x^2 - 4500 *x^3 - 5100*x^4 - 900*x^5 + 3600*x^6 + 2400*x^7 - 900*x^8 - 900*x^9 + 300* x^10)*Log[x]))/(-1 - 6*x - 15*x^2 - 17*x^3 - 3*x^4 + 12*x^5 + 8*x^6 - 3*x^ 7 - 3*x^8 + x^9),x]
Output:
75*(2*x + x^2 + E^(2*Log[x]^2)*x^2 + (28 + 69*x + 60*x^2)/(1 + 2*x + x^2 - x^3)^2 + (2*E^Log[x]^2*x^5)/(1 + 2*x + x^2 - x^3) - (35 + 29*x + 18*x^2)/ (1 + 2*x + x^2 - x^3))
Leaf count is larger than twice the leaf count of optimal. \(90\) vs. \(2(31)=62\).
Time = 2.00 (sec) , antiderivative size = 90, normalized size of antiderivative = 2.90, number of steps used = 5, number of rules used = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.019, Rules used = {2463, 7239, 27, 7293, 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.
| \(\displaystyle \int \frac {150 x^{10}-300 x^9-900 x^8-600 x^7+e^{\log ^2(x)} \left (-300 x^{10}+750 x^9+1350 x^8-1050 x^7-3600 x^6-2700 x^5-750 x^4+\left (-300 x^{10}+600 x^9+900 x^8-600 x^7-1800 x^6-1200 x^5-300 x^4\right ) \log (x)\right )+e^{2 \log ^2(x)} \left (150 x^{10}-450 x^9-450 x^8+1200 x^7+1800 x^6-450 x^5-2550 x^4-2250 x^3-900 x^2+\left (300 x^{10}-900 x^9-900 x^8+2400 x^7+3600 x^6-900 x^5-5100 x^4-4500 x^3-1800 x^2-300 x\right ) \log (x)-150 x\right )}{x^9-3 x^8-3 x^7+8 x^6+12 x^5-3 x^4-17 x^3-15 x^2-6 x-1} \, dx\) |
| \(\Big \downarrow \) 2463 |
| \(\displaystyle \int \frac {150 x^{10}-300 x^9-900 x^8-600 x^7+e^{\log ^2(x)} \left (-300 x^{10}+750 x^9+1350 x^8-1050 x^7-3600 x^6-2700 x^5-750 x^4+\left (-300 x^{10}+600 x^9+900 x^8-600 x^7-1800 x^6-1200 x^5-300 x^4\right ) \log (x)\right )+e^{2 \log ^2(x)} \left (150 x^{10}-450 x^9-450 x^8+1200 x^7+1800 x^6-450 x^5-2550 x^4-2250 x^3-900 x^2+\left (300 x^{10}-900 x^9-900 x^8+2400 x^7+3600 x^6-900 x^5-5100 x^4-4500 x^3-1800 x^2-300 x\right ) \log (x)-150 x\right )}{\left (x^3-x^2-2 x-1\right )^3}dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {150 x \left (x^3-\left (x^3-x^2-2 x-1\right ) e^{\log ^2(x)}\right ) \left (\left (-x^3+2 x^2+6 x+4\right ) x^3+\left (-x^3+x^2+2 x+1\right )^2 e^{\log ^2(x)}+2 \left (-x^3+x^2+2 x+1\right )^2 e^{\log ^2(x)} \log (x)\right )}{\left (-x^3+x^2+2 x+1\right )^3}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 150 \int \frac {x \left (x^3+e^{\log ^2(x)} \left (-x^3+x^2+2 x+1\right )\right ) \left (\left (-x^3+2 x^2+6 x+4\right ) x^3+e^{\log ^2(x)} \left (-x^3+x^2+2 x+1\right )^2+2 e^{\log ^2(x)} \left (-x^3+x^2+2 x+1\right )^2 \log (x)\right )}{\left (-x^3+x^2+2 x+1\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 150 \int \left (\frac {\left (x^3-2 x^2-6 x-4\right ) x^7}{\left (x^3-x^2-2 x-1\right )^3}-\frac {e^{\log ^2(x)} \left (2 \log (x) x^3+2 x^3-2 \log (x) x^2-3 x^2-4 \log (x) x-8 x-2 \log (x)-5\right ) x^4}{\left (x^3-x^2-2 x-1\right )^2}+e^{2 \log ^2(x)} (2 \log (x)+1) x\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle 150 \left (\frac {1}{2} x^2 e^{2 \log ^2(x)}+\frac {x^8}{2 \left (-x^3+x^2+2 x+1\right )^2}+\frac {x^5 e^{\log ^2(x)} \left (x^3 (-\log (x))+x^2 \log (x)+2 x \log (x)+\log (x)\right )}{\left (-x^3+x^2+2 x+1\right )^2 \log (x)}\right )\) |
Input:
Int[(-600*x^7 - 900*x^8 - 300*x^9 + 150*x^10 + E^Log[x]^2*(-750*x^4 - 2700 *x^5 - 3600*x^6 - 1050*x^7 + 1350*x^8 + 750*x^9 - 300*x^10 + (-300*x^4 - 1 200*x^5 - 1800*x^6 - 600*x^7 + 900*x^8 + 600*x^9 - 300*x^10)*Log[x]) + E^( 2*Log[x]^2)*(-150*x - 900*x^2 - 2250*x^3 - 2550*x^4 - 450*x^5 + 1800*x^6 + 1200*x^7 - 450*x^8 - 450*x^9 + 150*x^10 + (-300*x - 1800*x^2 - 4500*x^3 - 5100*x^4 - 900*x^5 + 3600*x^6 + 2400*x^7 - 900*x^8 - 900*x^9 + 300*x^10)* Log[x]))/(-1 - 6*x - 15*x^2 - 17*x^3 - 3*x^4 + 12*x^5 + 8*x^6 - 3*x^7 - 3* x^8 + x^9),x]
Output:
150*((E^(2*Log[x]^2)*x^2)/2 + x^8/(2*(1 + 2*x + x^2 - x^3)^2) + (E^Log[x]^ 2*x^5*(Log[x] + 2*x*Log[x] + x^2*Log[x] - x^3*Log[x]))/((1 + 2*x + x^2 - x ^3)^2*Log[x]))
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[(u_.)*(Px_)^(p_), x_Symbol] :> With[{Qx = Factor[Px]}, Int[ExpandIntegr and[u, Qx^p, x], x] /; !SumQ[NonfreeFactors[Qx, x]]] /; PolyQ[Px, x] && Gt Q[Expon[Px, x], 2] && !BinomialQ[Px, x] && !TrinomialQ[Px, x] && ILtQ[p, 0]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Leaf count of result is larger than twice the leaf count of optimal. \(102\) vs. \(2(30)=60\).
Time = 13.02 (sec) , antiderivative size = 103, normalized size of antiderivative = 3.32
| method | result | size |
| risch | \(75 x^{2}+150 x +\frac {1350 x^{5}+825 x^{4}-2250 x^{3}-3825 x^{2}-2250 x -525}{x^{6}-2 x^{5}-3 x^{4}+2 x^{3}+6 x^{2}+4 x +1}+75 \,{\mathrm e}^{2 \ln \left (x \right )^{2}} x^{2}-\frac {150 x^{5} {\mathrm e}^{\ln \left (x \right )^{2}}}{x^{3}-x^{2}-2 x -1}\) | \(103\) |
| parallelrisch | \(\frac {450 x^{8}+2700 \,{\mathrm e}^{2 \ln \left (x \right )^{2}} x^{4}+900 \,{\mathrm e}^{\ln \left (x \right )^{2}} x^{5}+1800 \,{\mathrm e}^{2 \ln \left (x \right )^{2}} x^{3}+450 \,{\mathrm e}^{2 \ln \left (x \right )^{2}} x^{2}+450 \,{\mathrm e}^{2 \ln \left (x \right )^{2}} x^{8}-900 \,{\mathrm e}^{2 \ln \left (x \right )^{2}} x^{7}-900 \,{\mathrm e}^{\ln \left (x \right )^{2}} x^{8}-1350 \,{\mathrm e}^{2 \ln \left (x \right )^{2}} x^{6}+900 \,{\mathrm e}^{\ln \left (x \right )^{2}} x^{7}+900 \,{\mathrm e}^{2 \ln \left (x \right )^{2}} x^{5}+1800 \,{\mathrm e}^{\ln \left (x \right )^{2}} x^{6}}{6 x^{6}-12 x^{5}-18 x^{4}+12 x^{3}+36 x^{2}+24 x +6}\) | \(163\) |
Input:
int((((300*x^10-900*x^9-900*x^8+2400*x^7+3600*x^6-900*x^5-5100*x^4-4500*x^ 3-1800*x^2-300*x)*ln(x)+150*x^10-450*x^9-450*x^8+1200*x^7+1800*x^6-450*x^5 -2550*x^4-2250*x^3-900*x^2-150*x)*exp(ln(x)^2)^2+((-300*x^10+600*x^9+900*x ^8-600*x^7-1800*x^6-1200*x^5-300*x^4)*ln(x)-300*x^10+750*x^9+1350*x^8-1050 *x^7-3600*x^6-2700*x^5-750*x^4)*exp(ln(x)^2)+150*x^10-300*x^9-900*x^8-600* x^7)/(x^9-3*x^8-3*x^7+8*x^6+12*x^5-3*x^4-17*x^3-15*x^2-6*x-1),x,method=_RE TURNVERBOSE)
Output:
75*x^2+150*x+(1350*x^5+825*x^4-2250*x^3-3825*x^2-2250*x-525)/(x^6-2*x^5-3* x^4+2*x^3+6*x^2+4*x+1)+75*exp(ln(x)^2)^2*x^2-150*x^5/(x^3-x^2-2*x-1)*exp(l n(x)^2)
Leaf count of result is larger than twice the leaf count of optimal. 131 vs. \(2 (31) = 62\).
Time = 0.09 (sec) , antiderivative size = 131, normalized size of antiderivative = 4.23 \[ \int \frac {-600 x^7-900 x^8-300 x^9+150 x^{10}+e^{\log ^2(x)} \left (-750 x^4-2700 x^5-3600 x^6-1050 x^7+1350 x^8+750 x^9-300 x^{10}+\left (-300 x^4-1200 x^5-1800 x^6-600 x^7+900 x^8+600 x^9-300 x^{10}\right ) \log (x)\right )+e^{2 \log ^2(x)} \left (-150 x-900 x^2-2250 x^3-2550 x^4-450 x^5+1800 x^6+1200 x^7-450 x^8-450 x^9+150 x^{10}+\left (-300 x-1800 x^2-4500 x^3-5100 x^4-900 x^5+3600 x^6+2400 x^7-900 x^8-900 x^9+300 x^{10}\right ) \log (x)\right )}{-1-6 x-15 x^2-17 x^3-3 x^4+12 x^5+8 x^6-3 x^7-3 x^8+x^9} \, dx=\frac {75 \, {\left (x^{8} - 7 \, x^{6} + 14 \, x^{5} + 21 \, x^{4} - 14 \, x^{3} - 42 \, x^{2} + {\left (x^{8} - 2 \, x^{7} - 3 \, x^{6} + 2 \, x^{5} + 6 \, x^{4} + 4 \, x^{3} + x^{2}\right )} e^{\left (2 \, \log \left (x\right )^{2}\right )} - 2 \, {\left (x^{8} - x^{7} - 2 \, x^{6} - x^{5}\right )} e^{\left (\log \left (x\right )^{2}\right )} - 28 \, x - 7\right )}}{x^{6} - 2 \, x^{5} - 3 \, x^{4} + 2 \, x^{3} + 6 \, x^{2} + 4 \, x + 1} \] Input:
integrate((((300*x^10-900*x^9-900*x^8+2400*x^7+3600*x^6-900*x^5-5100*x^4-4 500*x^3-1800*x^2-300*x)*log(x)+150*x^10-450*x^9-450*x^8+1200*x^7+1800*x^6- 450*x^5-2550*x^4-2250*x^3-900*x^2-150*x)*exp(log(x)^2)^2+((-300*x^10+600*x ^9+900*x^8-600*x^7-1800*x^6-1200*x^5-300*x^4)*log(x)-300*x^10+750*x^9+1350 *x^8-1050*x^7-3600*x^6-2700*x^5-750*x^4)*exp(log(x)^2)+150*x^10-300*x^9-90 0*x^8-600*x^7)/(x^9-3*x^8-3*x^7+8*x^6+12*x^5-3*x^4-17*x^3-15*x^2-6*x-1),x, algorithm="fricas")
Output:
75*(x^8 - 7*x^6 + 14*x^5 + 21*x^4 - 14*x^3 - 42*x^2 + (x^8 - 2*x^7 - 3*x^6 + 2*x^5 + 6*x^4 + 4*x^3 + x^2)*e^(2*log(x)^2) - 2*(x^8 - x^7 - 2*x^6 - x^ 5)*e^(log(x)^2) - 28*x - 7)/(x^6 - 2*x^5 - 3*x^4 + 2*x^3 + 6*x^2 + 4*x + 1 )
Leaf count of result is larger than twice the leaf count of optimal. 114 vs. \(2 (24) = 48\).
Time = 0.24 (sec) , antiderivative size = 114, normalized size of antiderivative = 3.68 \[ \int \frac {-600 x^7-900 x^8-300 x^9+150 x^{10}+e^{\log ^2(x)} \left (-750 x^4-2700 x^5-3600 x^6-1050 x^7+1350 x^8+750 x^9-300 x^{10}+\left (-300 x^4-1200 x^5-1800 x^6-600 x^7+900 x^8+600 x^9-300 x^{10}\right ) \log (x)\right )+e^{2 \log ^2(x)} \left (-150 x-900 x^2-2250 x^3-2550 x^4-450 x^5+1800 x^6+1200 x^7-450 x^8-450 x^9+150 x^{10}+\left (-300 x-1800 x^2-4500 x^3-5100 x^4-900 x^5+3600 x^6+2400 x^7-900 x^8-900 x^9+300 x^{10}\right ) \log (x)\right )}{-1-6 x-15 x^2-17 x^3-3 x^4+12 x^5+8 x^6-3 x^7-3 x^8+x^9} \, dx=75 x^{2} + 150 x + \frac {- 150 x^{5} e^{\log {\left (x \right )}^{2}} + \left (75 x^{5} - 75 x^{4} - 150 x^{3} - 75 x^{2}\right ) e^{2 \log {\left (x \right )}^{2}}}{x^{3} - x^{2} - 2 x - 1} + \frac {1350 x^{5} + 825 x^{4} - 2250 x^{3} - 3825 x^{2} - 2250 x - 525}{x^{6} - 2 x^{5} - 3 x^{4} + 2 x^{3} + 6 x^{2} + 4 x + 1} \] Input:
integrate((((300*x**10-900*x**9-900*x**8+2400*x**7+3600*x**6-900*x**5-5100 *x**4-4500*x**3-1800*x**2-300*x)*ln(x)+150*x**10-450*x**9-450*x**8+1200*x* *7+1800*x**6-450*x**5-2550*x**4-2250*x**3-900*x**2-150*x)*exp(ln(x)**2)**2 +((-300*x**10+600*x**9+900*x**8-600*x**7-1800*x**6-1200*x**5-300*x**4)*ln( x)-300*x**10+750*x**9+1350*x**8-1050*x**7-3600*x**6-2700*x**5-750*x**4)*ex p(ln(x)**2)+150*x**10-300*x**9-900*x**8-600*x**7)/(x**9-3*x**8-3*x**7+8*x* *6+12*x**5-3*x**4-17*x**3-15*x**2-6*x-1),x)
Output:
75*x**2 + 150*x + (-150*x**5*exp(log(x)**2) + (75*x**5 - 75*x**4 - 150*x** 3 - 75*x**2)*exp(2*log(x)**2))/(x**3 - x**2 - 2*x - 1) + (1350*x**5 + 825* x**4 - 2250*x**3 - 3825*x**2 - 2250*x - 525)/(x**6 - 2*x**5 - 3*x**4 + 2*x **3 + 6*x**2 + 4*x + 1)
Leaf count of result is larger than twice the leaf count of optimal. 131 vs. \(2 (31) = 62\).
Time = 0.05 (sec) , antiderivative size = 131, normalized size of antiderivative = 4.23 \[ \int \frac {-600 x^7-900 x^8-300 x^9+150 x^{10}+e^{\log ^2(x)} \left (-750 x^4-2700 x^5-3600 x^6-1050 x^7+1350 x^8+750 x^9-300 x^{10}+\left (-300 x^4-1200 x^5-1800 x^6-600 x^7+900 x^8+600 x^9-300 x^{10}\right ) \log (x)\right )+e^{2 \log ^2(x)} \left (-150 x-900 x^2-2250 x^3-2550 x^4-450 x^5+1800 x^6+1200 x^7-450 x^8-450 x^9+150 x^{10}+\left (-300 x-1800 x^2-4500 x^3-5100 x^4-900 x^5+3600 x^6+2400 x^7-900 x^8-900 x^9+300 x^{10}\right ) \log (x)\right )}{-1-6 x-15 x^2-17 x^3-3 x^4+12 x^5+8 x^6-3 x^7-3 x^8+x^9} \, dx=\frac {75 \, {\left (x^{8} - 7 \, x^{6} + 14 \, x^{5} + 21 \, x^{4} - 14 \, x^{3} - 42 \, x^{2} + {\left (x^{8} - 2 \, x^{7} - 3 \, x^{6} + 2 \, x^{5} + 6 \, x^{4} + 4 \, x^{3} + x^{2}\right )} e^{\left (2 \, \log \left (x\right )^{2}\right )} - 2 \, {\left (x^{8} - x^{7} - 2 \, x^{6} - x^{5}\right )} e^{\left (\log \left (x\right )^{2}\right )} - 28 \, x - 7\right )}}{x^{6} - 2 \, x^{5} - 3 \, x^{4} + 2 \, x^{3} + 6 \, x^{2} + 4 \, x + 1} \] Input:
integrate((((300*x^10-900*x^9-900*x^8+2400*x^7+3600*x^6-900*x^5-5100*x^4-4 500*x^3-1800*x^2-300*x)*log(x)+150*x^10-450*x^9-450*x^8+1200*x^7+1800*x^6- 450*x^5-2550*x^4-2250*x^3-900*x^2-150*x)*exp(log(x)^2)^2+((-300*x^10+600*x ^9+900*x^8-600*x^7-1800*x^6-1200*x^5-300*x^4)*log(x)-300*x^10+750*x^9+1350 *x^8-1050*x^7-3600*x^6-2700*x^5-750*x^4)*exp(log(x)^2)+150*x^10-300*x^9-90 0*x^8-600*x^7)/(x^9-3*x^8-3*x^7+8*x^6+12*x^5-3*x^4-17*x^3-15*x^2-6*x-1),x, algorithm="maxima")
Output:
75*(x^8 - 7*x^6 + 14*x^5 + 21*x^4 - 14*x^3 - 42*x^2 + (x^8 - 2*x^7 - 3*x^6 + 2*x^5 + 6*x^4 + 4*x^3 + x^2)*e^(2*log(x)^2) - 2*(x^8 - x^7 - 2*x^6 - x^ 5)*e^(log(x)^2) - 28*x - 7)/(x^6 - 2*x^5 - 3*x^4 + 2*x^3 + 6*x^2 + 4*x + 1 )
\[ \int \frac {-600 x^7-900 x^8-300 x^9+150 x^{10}+e^{\log ^2(x)} \left (-750 x^4-2700 x^5-3600 x^6-1050 x^7+1350 x^8+750 x^9-300 x^{10}+\left (-300 x^4-1200 x^5-1800 x^6-600 x^7+900 x^8+600 x^9-300 x^{10}\right ) \log (x)\right )+e^{2 \log ^2(x)} \left (-150 x-900 x^2-2250 x^3-2550 x^4-450 x^5+1800 x^6+1200 x^7-450 x^8-450 x^9+150 x^{10}+\left (-300 x-1800 x^2-4500 x^3-5100 x^4-900 x^5+3600 x^6+2400 x^7-900 x^8-900 x^9+300 x^{10}\right ) \log (x)\right )}{-1-6 x-15 x^2-17 x^3-3 x^4+12 x^5+8 x^6-3 x^7-3 x^8+x^9} \, dx=\int { \frac {150 \, {\left (x^{10} - 2 \, x^{9} - 6 \, x^{8} - 4 \, x^{7} + {\left (x^{10} - 3 \, x^{9} - 3 \, x^{8} + 8 \, x^{7} + 12 \, x^{6} - 3 \, x^{5} - 17 \, x^{4} - 15 \, x^{3} - 6 \, x^{2} + 2 \, {\left (x^{10} - 3 \, x^{9} - 3 \, x^{8} + 8 \, x^{7} + 12 \, x^{6} - 3 \, x^{5} - 17 \, x^{4} - 15 \, x^{3} - 6 \, x^{2} - x\right )} \log \left (x\right ) - x\right )} e^{\left (2 \, \log \left (x\right )^{2}\right )} - {\left (2 \, x^{10} - 5 \, x^{9} - 9 \, x^{8} + 7 \, x^{7} + 24 \, x^{6} + 18 \, x^{5} + 5 \, x^{4} + 2 \, {\left (x^{10} - 2 \, x^{9} - 3 \, x^{8} + 2 \, x^{7} + 6 \, x^{6} + 4 \, x^{5} + x^{4}\right )} \log \left (x\right )\right )} e^{\left (\log \left (x\right )^{2}\right )}\right )}}{x^{9} - 3 \, x^{8} - 3 \, x^{7} + 8 \, x^{6} + 12 \, x^{5} - 3 \, x^{4} - 17 \, x^{3} - 15 \, x^{2} - 6 \, x - 1} \,d x } \] Input:
integrate((((300*x^10-900*x^9-900*x^8+2400*x^7+3600*x^6-900*x^5-5100*x^4-4 500*x^3-1800*x^2-300*x)*log(x)+150*x^10-450*x^9-450*x^8+1200*x^7+1800*x^6- 450*x^5-2550*x^4-2250*x^3-900*x^2-150*x)*exp(log(x)^2)^2+((-300*x^10+600*x ^9+900*x^8-600*x^7-1800*x^6-1200*x^5-300*x^4)*log(x)-300*x^10+750*x^9+1350 *x^8-1050*x^7-3600*x^6-2700*x^5-750*x^4)*exp(log(x)^2)+150*x^10-300*x^9-90 0*x^8-600*x^7)/(x^9-3*x^8-3*x^7+8*x^6+12*x^5-3*x^4-17*x^3-15*x^2-6*x-1),x, algorithm="giac")
Output:
integrate(150*(x^10 - 2*x^9 - 6*x^8 - 4*x^7 + (x^10 - 3*x^9 - 3*x^8 + 8*x^ 7 + 12*x^6 - 3*x^5 - 17*x^4 - 15*x^3 - 6*x^2 + 2*(x^10 - 3*x^9 - 3*x^8 + 8 *x^7 + 12*x^6 - 3*x^5 - 17*x^4 - 15*x^3 - 6*x^2 - x)*log(x) - x)*e^(2*log( x)^2) - (2*x^10 - 5*x^9 - 9*x^8 + 7*x^7 + 24*x^6 + 18*x^5 + 5*x^4 + 2*(x^1 0 - 2*x^9 - 3*x^8 + 2*x^7 + 6*x^6 + 4*x^5 + x^4)*log(x))*e^(log(x)^2))/(x^ 9 - 3*x^8 - 3*x^7 + 8*x^6 + 12*x^5 - 3*x^4 - 17*x^3 - 15*x^2 - 6*x - 1), x )
Time = 3.27 (sec) , antiderivative size = 103, normalized size of antiderivative = 3.32 \[ \int \frac {-600 x^7-900 x^8-300 x^9+150 x^{10}+e^{\log ^2(x)} \left (-750 x^4-2700 x^5-3600 x^6-1050 x^7+1350 x^8+750 x^9-300 x^{10}+\left (-300 x^4-1200 x^5-1800 x^6-600 x^7+900 x^8+600 x^9-300 x^{10}\right ) \log (x)\right )+e^{2 \log ^2(x)} \left (-150 x-900 x^2-2250 x^3-2550 x^4-450 x^5+1800 x^6+1200 x^7-450 x^8-450 x^9+150 x^{10}+\left (-300 x-1800 x^2-4500 x^3-5100 x^4-900 x^5+3600 x^6+2400 x^7-900 x^8-900 x^9+300 x^{10}\right ) \log (x)\right )}{-1-6 x-15 x^2-17 x^3-3 x^4+12 x^5+8 x^6-3 x^7-3 x^8+x^9} \, dx=150\,x+75\,x^2\,{\mathrm {e}}^{2\,{\ln \left (x\right )}^2}-\frac {-1350\,x^5-825\,x^4+2250\,x^3+3825\,x^2+2250\,x+525}{x^6-2\,x^5-3\,x^4+2\,x^3+6\,x^2+4\,x+1}+75\,x^2+\frac {150\,x^5\,{\mathrm {e}}^{{\ln \left (x\right )}^2}}{-x^3+x^2+2\,x+1} \] Input:
int((exp(log(x)^2)*(log(x)*(300*x^4 + 1200*x^5 + 1800*x^6 + 600*x^7 - 900* x^8 - 600*x^9 + 300*x^10) + 750*x^4 + 2700*x^5 + 3600*x^6 + 1050*x^7 - 135 0*x^8 - 750*x^9 + 300*x^10) + 600*x^7 + 900*x^8 + 300*x^9 - 150*x^10 + exp (2*log(x)^2)*(150*x + log(x)*(300*x + 1800*x^2 + 4500*x^3 + 5100*x^4 + 900 *x^5 - 3600*x^6 - 2400*x^7 + 900*x^8 + 900*x^9 - 300*x^10) + 900*x^2 + 225 0*x^3 + 2550*x^4 + 450*x^5 - 1800*x^6 - 1200*x^7 + 450*x^8 + 450*x^9 - 150 *x^10))/(6*x + 15*x^2 + 17*x^3 + 3*x^4 - 12*x^5 - 8*x^6 + 3*x^7 + 3*x^8 - x^9 + 1),x)
Output:
150*x + 75*x^2*exp(2*log(x)^2) - (2250*x + 3825*x^2 + 2250*x^3 - 825*x^4 - 1350*x^5 + 525)/(4*x + 6*x^2 + 2*x^3 - 3*x^4 - 2*x^5 + x^6 + 1) + 75*x^2 + (150*x^5*exp(log(x)^2))/(2*x + x^2 - x^3 + 1)
Time = 0.15 (sec) , antiderivative size = 166, normalized size of antiderivative = 5.35 \[ \int \frac {-600 x^7-900 x^8-300 x^9+150 x^{10}+e^{\log ^2(x)} \left (-750 x^4-2700 x^5-3600 x^6-1050 x^7+1350 x^8+750 x^9-300 x^{10}+\left (-300 x^4-1200 x^5-1800 x^6-600 x^7+900 x^8+600 x^9-300 x^{10}\right ) \log (x)\right )+e^{2 \log ^2(x)} \left (-150 x-900 x^2-2250 x^3-2550 x^4-450 x^5+1800 x^6+1200 x^7-450 x^8-450 x^9+150 x^{10}+\left (-300 x-1800 x^2-4500 x^3-5100 x^4-900 x^5+3600 x^6+2400 x^7-900 x^8-900 x^9+300 x^{10}\right ) \log (x)\right )}{-1-6 x-15 x^2-17 x^3-3 x^4+12 x^5+8 x^6-3 x^7-3 x^8+x^9} \, dx=\frac {75 x^{2} \left (e^{2 \mathrm {log}\left (x \right )^{2}} x^{6}-2 e^{2 \mathrm {log}\left (x \right )^{2}} x^{5}-3 e^{2 \mathrm {log}\left (x \right )^{2}} x^{4}+2 e^{2 \mathrm {log}\left (x \right )^{2}} x^{3}+6 e^{2 \mathrm {log}\left (x \right )^{2}} x^{2}+4 e^{2 \mathrm {log}\left (x \right )^{2}} x +e^{2 \mathrm {log}\left (x \right )^{2}}-2 e^{\mathrm {log}\left (x \right )^{2}} x^{6}+2 e^{\mathrm {log}\left (x \right )^{2}} x^{5}+4 e^{\mathrm {log}\left (x \right )^{2}} x^{4}+2 e^{\mathrm {log}\left (x \right )^{2}} x^{3}+x^{6}\right )}{x^{6}-2 x^{5}-3 x^{4}+2 x^{3}+6 x^{2}+4 x +1} \] Input:
int((((300*x^10-900*x^9-900*x^8+2400*x^7+3600*x^6-900*x^5-5100*x^4-4500*x^ 3-1800*x^2-300*x)*log(x)+150*x^10-450*x^9-450*x^8+1200*x^7+1800*x^6-450*x^ 5-2550*x^4-2250*x^3-900*x^2-150*x)*exp(log(x)^2)^2+((-300*x^10+600*x^9+900 *x^8-600*x^7-1800*x^6-1200*x^5-300*x^4)*log(x)-300*x^10+750*x^9+1350*x^8-1 050*x^7-3600*x^6-2700*x^5-750*x^4)*exp(log(x)^2)+150*x^10-300*x^9-900*x^8- 600*x^7)/(x^9-3*x^8-3*x^7+8*x^6+12*x^5-3*x^4-17*x^3-15*x^2-6*x-1),x)
Output:
(75*x**2*(e**(2*log(x)**2)*x**6 - 2*e**(2*log(x)**2)*x**5 - 3*e**(2*log(x) **2)*x**4 + 2*e**(2*log(x)**2)*x**3 + 6*e**(2*log(x)**2)*x**2 + 4*e**(2*lo g(x)**2)*x + e**(2*log(x)**2) - 2*e**(log(x)**2)*x**6 + 2*e**(log(x)**2)*x **5 + 4*e**(log(x)**2)*x**4 + 2*e**(log(x)**2)*x**3 + x**6))/(x**6 - 2*x** 5 - 3*x**4 + 2*x**3 + 6*x**2 + 4*x + 1)