Integrand size = 74, antiderivative size = 25 \[ \int \frac {-2560000 x^2-96000 x^3-20100 x^4-360 x^5-36 x^6+e^x \left (-240000+231000 x+1800 x^2+900 x^3\right )}{640000 x^2+24000 x^3+5025 x^4+90 x^5+9 x^6} \, dx=-4 x+\frac {e^x}{x \left (\frac {8}{3}+\frac {1}{100} x (5+x)\right )} \] Output:
exp(x)/x/(1/100*(5+x)*x+8/3)-4*x
Time = 0.38 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.44 \[ \int \frac {-2560000 x^2-96000 x^3-20100 x^4-360 x^5-36 x^6+e^x \left (-240000+231000 x+1800 x^2+900 x^3\right )}{640000 x^2+24000 x^3+5025 x^4+90 x^5+9 x^6} \, dx=-4 x+300 e^x \left (\frac {1}{800 x}-\frac {3 (5+x)}{800 \left (800+15 x+3 x^2\right )}\right ) \] Input:
Integrate[(-2560000*x^2 - 96000*x^3 - 20100*x^4 - 360*x^5 - 36*x^6 + E^x*( -240000 + 231000*x + 1800*x^2 + 900*x^3))/(640000*x^2 + 24000*x^3 + 5025*x ^4 + 90*x^5 + 9*x^6),x]
Output:
-4*x + 300*E^x*(1/(800*x) - (3*(5 + x))/(800*(800 + 15*x + 3*x^2)))
Result contains higher order function than in optimal. Order 4 vs. order 3 in optimal.
Time = 7.09 (sec) , antiderivative size = 1678, normalized size of antiderivative = 67.12, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.041, Rules used = {2026, 2463, 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.
| \(\displaystyle \int \frac {-36 x^6-360 x^5-20100 x^4-96000 x^3-2560000 x^2+e^x \left (900 x^3+1800 x^2+231000 x-240000\right )}{9 x^6+90 x^5+5025 x^4+24000 x^3+640000 x^2} \, dx\) |
| \(\Big \downarrow \) 2026 |
| \(\displaystyle \int \frac {-36 x^6-360 x^5-20100 x^4-96000 x^3-2560000 x^2+e^x \left (900 x^3+1800 x^2+231000 x-240000\right )}{x^2 \left (9 x^4+90 x^3+5025 x^2+24000 x+640000\right )}dx\) |
| \(\Big \downarrow \) 2463 |
| \(\displaystyle \int \left (\frac {4 i \sqrt {\frac {3}{5}} \left (-36 x^6-360 x^5-20100 x^4-96000 x^3-2560000 x^2+e^x \left (900 x^3+1800 x^2+231000 x-240000\right )\right )}{78125 x^2 \left (6 x+25 i \sqrt {15}+15\right )}+\frac {4 i \sqrt {\frac {3}{5}} \left (-36 x^6-360 x^5-20100 x^4-96000 x^3-2560000 x^2+e^x \left (900 x^3+1800 x^2+231000 x-240000\right )\right )}{78125 \left (-6 x+25 i \sqrt {15}-15\right ) x^2}-\frac {12 \left (-36 x^6-360 x^5-20100 x^4-96000 x^3-2560000 x^2+e^x \left (900 x^3+1800 x^2+231000 x-240000\right )\right )}{3125 \left (-6 x+25 i \sqrt {15}-15\right )^2 x^2}-\frac {12 \left (-36 x^6-360 x^5-20100 x^4-96000 x^3-2560000 x^2+e^x \left (900 x^3+1800 x^2+231000 x-240000\right )\right )}{3125 x^2 \left (6 x+25 i \sqrt {15}+15\right )^2}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -\frac {6 i \sqrt {\frac {3}{5}} \left (\frac {320}{3 i-5 \sqrt {15}}-i x\right )^4}{78125}-\frac {8 i \left (\frac {320}{3 i-5 \sqrt {15}}-i x\right )^3}{3125}+\frac {6 i \sqrt {\frac {3}{5}} \left (\frac {320}{3 i+5 \sqrt {15}}-i x\right )^4}{78125}-\frac {8 i \left (\frac {320}{3 i+5 \sqrt {15}}-i x\right )^3}{3125}+\frac {8 x^3}{3125}-\frac {2}{625} \left (3+5 i \sqrt {15}\right ) x^2-\frac {2}{625} \left (3-5 i \sqrt {15}\right ) x^2+\frac {24 x^2}{625}-\frac {6}{125} \left (61+5 i \sqrt {15}\right ) x-\frac {8}{125} \left (3+5 i \sqrt {15}\right ) x-\frac {6}{125} \left (61-5 i \sqrt {15}\right ) x-\frac {8}{125} \left (3-5 i \sqrt {15}\right ) x+\frac {536 x}{125}+\frac {144 e^{-\frac {5}{6} \left (3+5 i \sqrt {15}\right )} \operatorname {ExpIntegralEi}\left (-\frac {1}{6} i \left (6 i x+5 \left (3 i-5 \sqrt {15}\right )\right )\right )}{625 \left (3+5 i \sqrt {15}\right )}+\frac {72 \left (25-i \sqrt {15}\right ) e^{-\frac {5}{6} \left (3+5 i \sqrt {15}\right )} \operatorname {ExpIntegralEi}\left (-\frac {1}{6} i \left (6 i x+5 \left (3 i-5 \sqrt {15}\right )\right )\right )}{25 \left (3 i-5 \sqrt {15}\right )^2}-\frac {144 \left (2241 i-1495 \sqrt {15}\right ) e^{-\frac {5}{6} \left (3+5 i \sqrt {15}\right )} \operatorname {ExpIntegralEi}\left (-\frac {1}{6} i \left (6 i x+5 \left (3 i-5 \sqrt {15}\right )\right )\right )}{625 \left (3 i-5 \sqrt {15}\right )^3}-\frac {144 \left (2241 i+1495 \sqrt {15}\right ) e^{\frac {5}{6} i \left (3 i+5 \sqrt {15}\right )} \operatorname {ExpIntegralEi}\left (-\frac {1}{6} i \left (6 i x+5 \left (3 i+5 \sqrt {15}\right )\right )\right )}{625 \left (3 i+5 \sqrt {15}\right )^3}+\frac {72 \left (25+i \sqrt {15}\right ) e^{\frac {5}{6} i \left (3 i+5 \sqrt {15}\right )} \operatorname {ExpIntegralEi}\left (-\frac {1}{6} i \left (6 i x+5 \left (3 i+5 \sqrt {15}\right )\right )\right )}{25 \left (3 i+5 \sqrt {15}\right )^2}+\frac {144 e^{\frac {5}{6} i \left (3 i+5 \sqrt {15}\right )} \operatorname {ExpIntegralEi}\left (-\frac {1}{6} i \left (6 i x+5 \left (3 i+5 \sqrt {15}\right )\right )\right )}{625 \left (3-5 i \sqrt {15}\right )}+\frac {288 \left (423 i+385 \sqrt {15}\right ) \operatorname {ExpIntegralEi}(x)}{625 \left (3 i+5 \sqrt {15}\right )^3}-\frac {1536 \sqrt {\frac {3}{5}} \operatorname {ExpIntegralEi}(x)}{625 \left (3 i+5 \sqrt {15}\right )}+\frac {288 \left (1925+109 i \sqrt {15}\right ) \operatorname {ExpIntegralEi}(x)}{15625 \left (3 i+5 \sqrt {15}\right )^2}-\frac {4608 \operatorname {ExpIntegralEi}(x)}{125 \left (3 i+5 \sqrt {15}\right )^2}+\frac {288 \left (1925-109 i \sqrt {15}\right ) \operatorname {ExpIntegralEi}(x)}{15625 \left (3 i-5 \sqrt {15}\right )^2}+\frac {1536 \sqrt {\frac {3}{5}} \operatorname {ExpIntegralEi}(x)}{625 \left (3 i-5 \sqrt {15}\right )}-\frac {4608 \operatorname {ExpIntegralEi}(x)}{125 \left (3 i-5 \sqrt {15}\right )^2}+\frac {288 \left (423 i-385 \sqrt {15}\right ) \operatorname {ExpIntegralEi}(x)}{625 \left (3 i-5 \sqrt {15}\right )^3}+\frac {8}{75} \left (279+145 i \sqrt {15}\right ) \log \left (6 i x+5 \left (3 i-5 \sqrt {15}\right )\right )-\frac {268}{75} \left (3+5 i \sqrt {15}\right ) \log \left (6 i x+5 \left (3 i-5 \sqrt {15}\right )\right )-\frac {12}{25} \left (61-5 i \sqrt {15}\right ) \log \left (6 i x+5 \left (3 i-5 \sqrt {15}\right )\right )+\frac {256}{25} \log \left (6 i x+5 \left (3 i-5 \sqrt {15}\right )\right )+\frac {8}{75} \left (279-145 i \sqrt {15}\right ) \log \left (6 i x+5 \left (3 i+5 \sqrt {15}\right )\right )-\frac {12}{25} \left (61+5 i \sqrt {15}\right ) \log \left (6 i x+5 \left (3 i+5 \sqrt {15}\right )\right )-\frac {268}{75} \left (3-5 i \sqrt {15}\right ) \log \left (6 i x+5 \left (3 i+5 \sqrt {15}\right )\right )+\frac {256}{25} \log \left (6 i x+5 \left (3 i+5 \sqrt {15}\right )\right )-\frac {432 \left (25 i+\sqrt {15}\right ) e^x}{25 \left (3 i-5 \sqrt {15}\right )^2 \left (6 i x+5 \left (3 i-5 \sqrt {15}\right )\right )}-\frac {4 \left (1673 i+305 \sqrt {15}\right )}{5 \left (6 i x+5 \left (3 i-5 \sqrt {15}\right )\right )}+\frac {268 \left (61 i+5 \sqrt {15}\right )}{5 \left (6 i x+5 \left (3 i-5 \sqrt {15}\right )\right )}+\frac {256 \left (3 i-5 \sqrt {15}\right )}{5 \left (6 i x+5 \left (3 i-5 \sqrt {15}\right )\right )}-\frac {8 \left (279 i-145 \sqrt {15}\right )}{5 \left (6 i x+5 \left (3 i-5 \sqrt {15}\right )\right )}-\frac {8192 i}{5 \left (6 i x+5 \left (3 i-5 \sqrt {15}\right )\right )}-\frac {432 \left (25 i-\sqrt {15}\right ) e^x}{25 \left (3 i+5 \sqrt {15}\right )^2 \left (6 i x+5 \left (3 i+5 \sqrt {15}\right )\right )}-\frac {8 \left (279 i+145 \sqrt {15}\right )}{5 \left (6 i x+5 \left (3 i+5 \sqrt {15}\right )\right )}+\frac {256 \left (3 i+5 \sqrt {15}\right )}{5 \left (6 i x+5 \left (3 i+5 \sqrt {15}\right )\right )}+\frac {268 \left (61 i-5 \sqrt {15}\right )}{5 \left (6 i x+5 \left (3 i+5 \sqrt {15}\right )\right )}-\frac {4 \left (1673 i-305 \sqrt {15}\right )}{5 \left (6 i x+5 \left (3 i+5 \sqrt {15}\right )\right )}-\frac {8192 i}{5 \left (6 i x+5 \left (3 i+5 \sqrt {15}\right )\right )}+\frac {1536 \sqrt {\frac {3}{5}} e^x}{625 \left (3 i+5 \sqrt {15}\right ) x}+\frac {4608 e^x}{125 \left (3 i+5 \sqrt {15}\right )^2 x}-\frac {1536 \sqrt {\frac {3}{5}} e^x}{625 \left (3 i-5 \sqrt {15}\right ) x}+\frac {4608 e^x}{125 \left (3 i-5 \sqrt {15}\right )^2 x}\) |
Input:
Int[(-2560000*x^2 - 96000*x^3 - 20100*x^4 - 360*x^5 - 36*x^6 + E^x*(-24000 0 + 231000*x + 1800*x^2 + 900*x^3))/(640000*x^2 + 24000*x^3 + 5025*x^4 + 9 0*x^5 + 9*x^6),x]
Output:
((-8*I)/3125)*(320/(3*I - 5*Sqrt[15]) - I*x)^3 - ((6*I)/78125)*Sqrt[3/5]*( 320/(3*I - 5*Sqrt[15]) - I*x)^4 - ((8*I)/3125)*(320/(3*I + 5*Sqrt[15]) - I *x)^3 + ((6*I)/78125)*Sqrt[3/5]*(320/(3*I + 5*Sqrt[15]) - I*x)^4 - ((8192* I)/5)/(5*(3*I - 5*Sqrt[15]) + (6*I)*x) - (8*(279*I - 145*Sqrt[15]))/(5*(5* (3*I - 5*Sqrt[15]) + (6*I)*x)) + (256*(3*I - 5*Sqrt[15]))/(5*(5*(3*I - 5*S qrt[15]) + (6*I)*x)) + (268*(61*I + 5*Sqrt[15]))/(5*(5*(3*I - 5*Sqrt[15]) + (6*I)*x)) - (4*(1673*I + 305*Sqrt[15]))/(5*(5*(3*I - 5*Sqrt[15]) + (6*I) *x)) - (432*(25*I + Sqrt[15])*E^x)/(25*(3*I - 5*Sqrt[15])^2*(5*(3*I - 5*Sq rt[15]) + (6*I)*x)) - ((8192*I)/5)/(5*(3*I + 5*Sqrt[15]) + (6*I)*x) - (4*( 1673*I - 305*Sqrt[15]))/(5*(5*(3*I + 5*Sqrt[15]) + (6*I)*x)) + (268*(61*I - 5*Sqrt[15]))/(5*(5*(3*I + 5*Sqrt[15]) + (6*I)*x)) + (256*(3*I + 5*Sqrt[1 5]))/(5*(5*(3*I + 5*Sqrt[15]) + (6*I)*x)) - (8*(279*I + 145*Sqrt[15]))/(5* (5*(3*I + 5*Sqrt[15]) + (6*I)*x)) - (432*(25*I - Sqrt[15])*E^x)/(25*(3*I + 5*Sqrt[15])^2*(5*(3*I + 5*Sqrt[15]) + (6*I)*x)) + (4608*E^x)/(125*(3*I - 5*Sqrt[15])^2*x) - (1536*Sqrt[3/5]*E^x)/(625*(3*I - 5*Sqrt[15])*x) + (4608 *E^x)/(125*(3*I + 5*Sqrt[15])^2*x) + (1536*Sqrt[3/5]*E^x)/(625*(3*I + 5*Sq rt[15])*x) + (536*x)/125 - (8*(3 - (5*I)*Sqrt[15])*x)/125 - (6*(61 - (5*I) *Sqrt[15])*x)/125 - (8*(3 + (5*I)*Sqrt[15])*x)/125 - (6*(61 + (5*I)*Sqrt[1 5])*x)/125 + (24*x^2)/625 - (2*(3 - (5*I)*Sqrt[15])*x^2)/625 - (2*(3 + (5* I)*Sqrt[15])*x^2)/625 + (8*x^3)/3125 - (144*(2241*I - 1495*Sqrt[15])*Ex...
Int[(Fx_.)*(Px_)^(p_.), x_Symbol] :> With[{r = Expon[Px, x, Min]}, Int[x^(p *r)*ExpandToSum[Px/x^r, x]^p*Fx, x] /; IGtQ[r, 0]] /; PolyQ[Px, x] && Integ erQ[p] && !MonomialQ[Px, x] && (ILtQ[p, 0] || !PolyQ[u, 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]
Time = 0.50 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.96
| method | result | size |
| risch | \(-4 x +\frac {300 \,{\mathrm e}^{x}}{x \left (3 x^{2}+15 x +800\right )}\) | \(24\) |
| norman | \(\frac {-2900 x^{2}+16000 x -12 x^{4}+300 \,{\mathrm e}^{x}}{x \left (3 x^{2}+15 x +800\right )}\) | \(35\) |
| parallelrisch | \(-\frac {36 x^{4}+8700 x^{2}-48000 x -900 \,{\mathrm e}^{x}}{3 x \left (3 x^{2}+15 x +800\right )}\) | \(36\) |
| parts | \(-4 x +\frac {72 \,{\mathrm e}^{x} \left (5+2 x \right )}{125 \left (3 x^{2}+15 x +800\right )}+\frac {3 \,{\mathrm e}^{x} \left (279 x^{2}+1635 x +50000\right )}{500 \left (3 x^{2}+15 x +800\right ) x}-\frac {231 \,{\mathrm e}^{x} \left (3 x -305\right )}{500 \left (3 x^{2}+15 x +800\right )}-\frac {12 \,{\mathrm e}^{x} \left (3 x +320\right )}{25 \left (3 x^{2}+15 x +800\right )}\) | \(97\) |
| default | \(-\frac {4096 \left (6 x +15\right )}{15 \left (3 x^{2}+15 x +800\right )}-\frac {256 \left (-15 x -1600\right )}{25 \left (3 x^{2}+15 x +800\right )}-\frac {20100 \left (-\frac {61 x}{1125}+\frac {32}{225}\right )}{x^{2}+5 x +\frac {800}{3}}-\frac {360 \left (\frac {31 x}{75}+\frac {1952}{135}\right )}{x^{2}+5 x +\frac {800}{3}}-4 x +\frac {-\frac {6692 x}{15}+3968}{x^{2}+5 x +\frac {800}{3}}+\frac {3 \,{\mathrm e}^{x} \left (279 x^{2}+1635 x +50000\right )}{500 \left (3 x^{2}+15 x +800\right ) x}-\frac {231 \,{\mathrm e}^{x} \left (3 x -305\right )}{500 \left (3 x^{2}+15 x +800\right )}+\frac {72 \,{\mathrm e}^{x} \left (5+2 x \right )}{125 \left (3 x^{2}+15 x +800\right )}-\frac {12 \,{\mathrm e}^{x} \left (3 x +320\right )}{25 \left (3 x^{2}+15 x +800\right )}\) | \(186\) |
| orering | \(\frac {\left (-1+x \right ) \left (\left (900 x^{3}+1800 x^{2}+231000 x -240000\right ) {\mathrm e}^{x}-36 x^{6}-360 x^{5}-20100 x^{4}-96000 x^{3}-2560000 x^{2}\right )}{9 x^{6}+90 x^{5}+5025 x^{4}+24000 x^{3}+640000 x^{2}}-\frac {\left (3 x^{4}+749 x^{2}-2370 x +800\right ) \left (3 x^{2}+15 x +800\right ) x \left (\frac {\left (2700 x^{2}+3600 x +231000\right ) {\mathrm e}^{x}+\left (900 x^{3}+1800 x^{2}+231000 x -240000\right ) {\mathrm e}^{x}-216 x^{5}-1800 x^{4}-80400 x^{3}-288000 x^{2}-5120000 x}{9 x^{6}+90 x^{5}+5025 x^{4}+24000 x^{3}+640000 x^{2}}-\frac {\left (\left (900 x^{3}+1800 x^{2}+231000 x -240000\right ) {\mathrm e}^{x}-36 x^{6}-360 x^{5}-20100 x^{4}-96000 x^{3}-2560000 x^{2}\right ) \left (54 x^{5}+450 x^{4}+20100 x^{3}+72000 x^{2}+1280000 x \right )}{\left (9 x^{6}+90 x^{5}+5025 x^{4}+24000 x^{3}+640000 x^{2}\right )^{2}}\right )}{9 x^{6}+36 x^{5}+4683 x^{4}+4620 x^{3}+583750 x^{2}-1208000 x +1280000}\) | \(321\) |
Input:
int(((900*x^3+1800*x^2+231000*x-240000)*exp(x)-36*x^6-360*x^5-20100*x^4-96 000*x^3-2560000*x^2)/(9*x^6+90*x^5+5025*x^4+24000*x^3+640000*x^2),x,method =_RETURNVERBOSE)
Output:
-4*x+300/x/(3*x^2+15*x+800)*exp(x)
Time = 0.09 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.52 \[ \int \frac {-2560000 x^2-96000 x^3-20100 x^4-360 x^5-36 x^6+e^x \left (-240000+231000 x+1800 x^2+900 x^3\right )}{640000 x^2+24000 x^3+5025 x^4+90 x^5+9 x^6} \, dx=-\frac {4 \, {\left (3 \, x^{4} + 15 \, x^{3} + 800 \, x^{2} - 75 \, e^{x}\right )}}{3 \, x^{3} + 15 \, x^{2} + 800 \, x} \] Input:
integrate(((900*x^3+1800*x^2+231000*x-240000)*exp(x)-36*x^6-360*x^5-20100* x^4-96000*x^3-2560000*x^2)/(9*x^6+90*x^5+5025*x^4+24000*x^3+640000*x^2),x, algorithm="fricas")
Output:
-4*(3*x^4 + 15*x^3 + 800*x^2 - 75*e^x)/(3*x^3 + 15*x^2 + 800*x)
Time = 0.06 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.80 \[ \int \frac {-2560000 x^2-96000 x^3-20100 x^4-360 x^5-36 x^6+e^x \left (-240000+231000 x+1800 x^2+900 x^3\right )}{640000 x^2+24000 x^3+5025 x^4+90 x^5+9 x^6} \, dx=- 4 x + \frac {300 e^{x}}{3 x^{3} + 15 x^{2} + 800 x} \] Input:
integrate(((900*x**3+1800*x**2+231000*x-240000)*exp(x)-36*x**6-360*x**5-20 100*x**4-96000*x**3-2560000*x**2)/(9*x**6+90*x**5+5025*x**4+24000*x**3+640 000*x**2),x)
Output:
-4*x + 300*exp(x)/(3*x**3 + 15*x**2 + 800*x)
Leaf count of result is larger than twice the leaf count of optimal. 119 vs. \(2 (21) = 42\).
Time = 0.16 (sec) , antiderivative size = 119, normalized size of antiderivative = 4.76 \[ \int \frac {-2560000 x^2-96000 x^3-20100 x^4-360 x^5-36 x^6+e^x \left (-240000+231000 x+1800 x^2+900 x^3\right )}{640000 x^2+24000 x^3+5025 x^4+90 x^5+9 x^6} \, dx=-4 \, x - \frac {4 \, {\left (1673 \, x - 14880\right )}}{5 \, {\left (3 \, x^{2} + 15 \, x + 800\right )}} - \frac {8 \, {\left (279 \, x + 9760\right )}}{5 \, {\left (3 \, x^{2} + 15 \, x + 800\right )}} + \frac {268 \, {\left (61 \, x - 160\right )}}{5 \, {\left (3 \, x^{2} + 15 \, x + 800\right )}} + \frac {256 \, {\left (3 \, x + 320\right )}}{5 \, {\left (3 \, x^{2} + 15 \, x + 800\right )}} - \frac {4096 \, {\left (2 \, x + 5\right )}}{5 \, {\left (3 \, x^{2} + 15 \, x + 800\right )}} + \frac {300 \, e^{x}}{3 \, x^{3} + 15 \, x^{2} + 800 \, x} \] Input:
integrate(((900*x^3+1800*x^2+231000*x-240000)*exp(x)-36*x^6-360*x^5-20100* x^4-96000*x^3-2560000*x^2)/(9*x^6+90*x^5+5025*x^4+24000*x^3+640000*x^2),x, algorithm="maxima")
Output:
-4*x - 4/5*(1673*x - 14880)/(3*x^2 + 15*x + 800) - 8/5*(279*x + 9760)/(3*x ^2 + 15*x + 800) + 268/5*(61*x - 160)/(3*x^2 + 15*x + 800) + 256/5*(3*x + 320)/(3*x^2 + 15*x + 800) - 4096/5*(2*x + 5)/(3*x^2 + 15*x + 800) + 300*e^ x/(3*x^3 + 15*x^2 + 800*x)
Time = 0.12 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.52 \[ \int \frac {-2560000 x^2-96000 x^3-20100 x^4-360 x^5-36 x^6+e^x \left (-240000+231000 x+1800 x^2+900 x^3\right )}{640000 x^2+24000 x^3+5025 x^4+90 x^5+9 x^6} \, dx=-\frac {4 \, {\left (3 \, x^{4} + 15 \, x^{3} + 800 \, x^{2} - 75 \, e^{x}\right )}}{3 \, x^{3} + 15 \, x^{2} + 800 \, x} \] Input:
integrate(((900*x^3+1800*x^2+231000*x-240000)*exp(x)-36*x^6-360*x^5-20100* x^4-96000*x^3-2560000*x^2)/(9*x^6+90*x^5+5025*x^4+24000*x^3+640000*x^2),x, algorithm="giac")
Output:
-4*(3*x^4 + 15*x^3 + 800*x^2 - 75*e^x)/(3*x^3 + 15*x^2 + 800*x)
Time = 6.99 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.92 \[ \int \frac {-2560000 x^2-96000 x^3-20100 x^4-360 x^5-36 x^6+e^x \left (-240000+231000 x+1800 x^2+900 x^3\right )}{640000 x^2+24000 x^3+5025 x^4+90 x^5+9 x^6} \, dx=\frac {300\,{\mathrm {e}}^x}{x\,\left (3\,x^2+15\,x+800\right )}-4\,x \] Input:
int(-(2560000*x^2 + 96000*x^3 + 20100*x^4 + 360*x^5 + 36*x^6 - exp(x)*(231 000*x + 1800*x^2 + 900*x^3 - 240000))/(640000*x^2 + 24000*x^3 + 5025*x^4 + 90*x^5 + 9*x^6),x)
Output:
(300*exp(x))/(x*(15*x + 3*x^2 + 800)) - 4*x
Time = 0.16 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.52 \[ \int \frac {-2560000 x^2-96000 x^3-20100 x^4-360 x^5-36 x^6+e^x \left (-240000+231000 x+1800 x^2+900 x^3\right )}{640000 x^2+24000 x^3+5025 x^4+90 x^5+9 x^6} \, dx=\frac {300 e^{x}-12 x^{4}-60 x^{3}-3200 x^{2}}{x \left (3 x^{2}+15 x +800\right )} \] Input:
int(((900*x^3+1800*x^2+231000*x-240000)*exp(x)-36*x^6-360*x^5-20100*x^4-96 000*x^3-2560000*x^2)/(9*x^6+90*x^5+5025*x^4+24000*x^3+640000*x^2),x)
Output:
(4*(75*e**x - 3*x**4 - 15*x**3 - 800*x**2))/(x*(3*x**2 + 15*x + 800))