Integrand size = 189, antiderivative size = 30 \[ \int \frac {-30 x^4+150 x^5+\left (-60 x^2+300 x^3\right ) \log (4)+(-30+150 x) \log ^2(4)+e^x \left (-3 x^4+\left (-6 x-3 x^2\right ) \log (4)\right )}{8 x^4+8 e^{2 x} x^4-160 x^5+1200 x^6-4000 x^7+5000 x^8+\left (16 x^2-320 x^3+2400 x^4-8000 x^5+10000 x^6\right ) \log (4)+\left (8-160 x+1200 x^2-4000 x^3+5000 x^4\right ) \log ^2(4)+e^x \left (-16 x^4+160 x^5-400 x^6+\left (-16 x^2+160 x^3-400 x^4\right ) \log (4)\right )} \, dx=\frac {3}{8 \left (-(1-5 x)^2+\frac {e^x}{1+\frac {\log (4)}{x^2}}\right )} \] Output:
3/(8*exp(x)/(1+2*ln(2)/x^2)-8*(-5*x+1)^2)
Time = 0.06 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.50 \[ \int \frac {-30 x^4+150 x^5+\left (-60 x^2+300 x^3\right ) \log (4)+(-30+150 x) \log ^2(4)+e^x \left (-3 x^4+\left (-6 x-3 x^2\right ) \log (4)\right )}{8 x^4+8 e^{2 x} x^4-160 x^5+1200 x^6-4000 x^7+5000 x^8+\left (16 x^2-320 x^3+2400 x^4-8000 x^5+10000 x^6\right ) \log (4)+\left (8-160 x+1200 x^2-4000 x^3+5000 x^4\right ) \log ^2(4)+e^x \left (-16 x^4+160 x^5-400 x^6+\left (-16 x^2+160 x^3-400 x^4\right ) \log (4)\right )} \, dx=-\frac {3 \left (x^2+\log (4)\right )}{8 \left (-10 x^3+25 x^4+\log (4)-10 x \log (4)+x^2 \left (1-e^x+25 \log (4)\right )\right )} \] Input:
Integrate[(-30*x^4 + 150*x^5 + (-60*x^2 + 300*x^3)*Log[4] + (-30 + 150*x)* Log[4]^2 + E^x*(-3*x^4 + (-6*x - 3*x^2)*Log[4]))/(8*x^4 + 8*E^(2*x)*x^4 - 160*x^5 + 1200*x^6 - 4000*x^7 + 5000*x^8 + (16*x^2 - 320*x^3 + 2400*x^4 - 8000*x^5 + 10000*x^6)*Log[4] + (8 - 160*x + 1200*x^2 - 4000*x^3 + 5000*x^4 )*Log[4]^2 + E^x*(-16*x^4 + 160*x^5 - 400*x^6 + (-16*x^2 + 160*x^3 - 400*x ^4)*Log[4])),x]
Output:
(-3*(x^2 + Log[4]))/(8*(-10*x^3 + 25*x^4 + Log[4] - 10*x*Log[4] + x^2*(1 - E^x + 25*Log[4])))
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.
| \(\displaystyle \int \frac {150 x^5-30 x^4+e^x \left (\left (-3 x^2-6 x\right ) \log (4)-3 x^4\right )+\left (300 x^3-60 x^2\right ) \log (4)+(150 x-30) \log ^2(4)}{5000 x^8-4000 x^7+1200 x^6-160 x^5+8 e^{2 x} x^4+8 x^4+\left (5000 x^4-4000 x^3+1200 x^2-160 x+8\right ) \log ^2(4)+e^x \left (-400 x^6+160 x^5-16 x^4+\left (-400 x^4+160 x^3-16 x^2\right ) \log (4)\right )+\left (10000 x^6-8000 x^5+2400 x^4-320 x^3+16 x^2\right ) \log (4)} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {3 \left (50 x^5-\left (e^x+10\right ) x^4+100 x^3 \log (4)-\left (e^x+20\right ) x^2 \log (4)-2 x \log (4) \left (e^x-25 \log (4)\right )-10 \log ^2(4)\right )}{8 \left (-25 x^4+10 x^3-x^2 \left (-e^x+1+25 \log (4)\right )+10 x \log (4)-\log (4)\right )^2}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {3}{8} \int -\frac {-50 x^5+\left (10+e^x\right ) x^4-100 \log (4) x^3+\left (20+e^x\right ) \log (4) x^2+2 \left (e^x-25 \log (4)\right ) \log (4) x+10 \log ^2(4)}{\left (-25 x^4+10 x^3-\left (1-e^x+25 \log (4)\right ) x^2+10 \log (4) x-\log (4)\right )^2}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -\frac {3}{8} \int \frac {-50 x^5+\left (10+e^x\right ) x^4-100 \log (4) x^3+\left (20+e^x\right ) \log (4) x^2+2 \left (e^x-25 \log (4)\right ) \log (4) x+10 \log ^2(4)}{\left (-25 x^4+10 x^3-\left (1-e^x+25 \log (4)\right ) x^2+10 \log (4) x-\log (4)\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {3}{8} \int \left (\frac {x^3+\log (4) x+\log (16)}{x \left (-25 x^4+10 x^3+e^x x^2-(1+25 \log (4)) x^2+10 \log (4) x-\log (4)\right )}+\frac {(1-5 x) \left (-5 x^6+11 x^5-10 \log (4) x^4+12 \log (4) x^3+2 \log (4) (1-\log (32)) x^2+\log ^2(4) x+2 \log ^2(4)\right )}{x \left (-25 x^4+10 x^3+e^x x^2-(1+25 \log (4)) x^2+10 \log (4) x-\log (4)\right )^2}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -\frac {3}{8} \left (-9 \log ^2(4) \int \frac {1}{\left (-25 x^4+10 x^3+e^x x^2-(1+25 \log (4)) x^2+10 \log (4) x-\log (4)\right )^2}dx+2 \log ^2(4) \int \frac {1}{x \left (-25 x^4+10 x^3+e^x x^2-(1+25 \log (4)) x^2+10 \log (4) x-\log (4)\right )^2}dx+2 \log (4) (1-\log (1024)) \int \frac {x}{\left (-25 x^4+10 x^3+e^x x^2-(1+25 \log (4)) x^2+10 \log (4) x-\log (4)\right )^2}dx+2 \log (4) (1+5 \log (32)) \int \frac {x^2}{\left (-25 x^4+10 x^3+e^x x^2-(1+25 \log (4)) x^2+10 \log (4) x-\log (4)\right )^2}dx-70 \log (4) \int \frac {x^3}{\left (-25 x^4+10 x^3+e^x x^2-(1+25 \log (4)) x^2+10 \log (4) x-\log (4)\right )^2}dx+(11+50 \log (4)) \int \frac {x^4}{\left (-25 x^4+10 x^3+e^x x^2-(1+25 \log (4)) x^2+10 \log (4) x-\log (4)\right )^2}dx+\log (4) \int \frac {1}{-25 x^4+10 x^3+e^x x^2-(1+25 \log (4)) x^2+10 \log (4) x-\log (4)}dx+\log (16) \int \frac {1}{x \left (-25 x^4+10 x^3+e^x x^2-(1+25 \log (4)) x^2+10 \log (4) x-\log (4)\right )}dx+\int \frac {x^2}{-25 x^4+10 x^3+e^x x^2-(1+25 \log (4)) x^2+10 \log (4) x-\log (4)}dx+25 \int \frac {x^6}{\left (-25 x^4+10 x^3+e^x x^2-(1+25 \log (4)) x^2+10 \log (4) x-\log (4)\right )^2}dx-60 \int \frac {x^5}{\left (-25 x^4+10 x^3+e^x x^2-(1+25 \log (4)) x^2+10 \log (4) x-\log (4)\right )^2}dx\right )\) |
Input:
Int[(-30*x^4 + 150*x^5 + (-60*x^2 + 300*x^3)*Log[4] + (-30 + 150*x)*Log[4] ^2 + E^x*(-3*x^4 + (-6*x - 3*x^2)*Log[4]))/(8*x^4 + 8*E^(2*x)*x^4 - 160*x^ 5 + 1200*x^6 - 4000*x^7 + 5000*x^8 + (16*x^2 - 320*x^3 + 2400*x^4 - 8000*x ^5 + 10000*x^6)*Log[4] + (8 - 160*x + 1200*x^2 - 4000*x^3 + 5000*x^4)*Log[ 4]^2 + E^x*(-16*x^4 + 160*x^5 - 400*x^6 + (-16*x^2 + 160*x^3 - 400*x^4)*Lo g[4])),x]
Output:
$Aborted
Time = 0.84 (sec) , antiderivative size = 50, normalized size of antiderivative = 1.67
| method | result | size |
| risch | \(-\frac {3 \left (x^{2}+2 \ln \left (2\right )\right )}{8 \left (25 x^{4}+50 x^{2} \ln \left (2\right )-{\mathrm e}^{x} x^{2}-10 x^{3}-20 x \ln \left (2\right )+x^{2}+2 \ln \left (2\right )\right )}\) | \(50\) |
| norman | \(\frac {-\frac {3 x^{2}}{8}-\frac {3 \ln \left (2\right )}{4}}{25 x^{4}+50 x^{2} \ln \left (2\right )-{\mathrm e}^{x} x^{2}-10 x^{3}-20 x \ln \left (2\right )+x^{2}+2 \ln \left (2\right )}\) | \(51\) |
| parallelrisch | \(-\frac {3 x^{2}+6 \ln \left (2\right )}{8 \left (25 x^{4}+50 x^{2} \ln \left (2\right )-{\mathrm e}^{x} x^{2}-10 x^{3}-20 x \ln \left (2\right )+x^{2}+2 \ln \left (2\right )\right )}\) | \(52\) |
Input:
int(((2*(-3*x^2-6*x)*ln(2)-3*x^4)*exp(x)+4*(150*x-30)*ln(2)^2+2*(300*x^3-6 0*x^2)*ln(2)+150*x^5-30*x^4)/(8*exp(x)^2*x^4+(2*(-400*x^4+160*x^3-16*x^2)* ln(2)-400*x^6+160*x^5-16*x^4)*exp(x)+4*(5000*x^4-4000*x^3+1200*x^2-160*x+8 )*ln(2)^2+2*(10000*x^6-8000*x^5+2400*x^4-320*x^3+16*x^2)*ln(2)+5000*x^8-40 00*x^7+1200*x^6-160*x^5+8*x^4),x,method=_RETURNVERBOSE)
Output:
-3/8*(x^2+2*ln(2))/(25*x^4+50*x^2*ln(2)-exp(x)*x^2-10*x^3-20*x*ln(2)+x^2+2 *ln(2))
Time = 0.09 (sec) , antiderivative size = 47, normalized size of antiderivative = 1.57 \[ \int \frac {-30 x^4+150 x^5+\left (-60 x^2+300 x^3\right ) \log (4)+(-30+150 x) \log ^2(4)+e^x \left (-3 x^4+\left (-6 x-3 x^2\right ) \log (4)\right )}{8 x^4+8 e^{2 x} x^4-160 x^5+1200 x^6-4000 x^7+5000 x^8+\left (16 x^2-320 x^3+2400 x^4-8000 x^5+10000 x^6\right ) \log (4)+\left (8-160 x+1200 x^2-4000 x^3+5000 x^4\right ) \log ^2(4)+e^x \left (-16 x^4+160 x^5-400 x^6+\left (-16 x^2+160 x^3-400 x^4\right ) \log (4)\right )} \, dx=-\frac {3 \, {\left (x^{2} + 2 \, \log \left (2\right )\right )}}{8 \, {\left (25 \, x^{4} - 10 \, x^{3} - x^{2} e^{x} + x^{2} + 2 \, {\left (25 \, x^{2} - 10 \, x + 1\right )} \log \left (2\right )\right )}} \] Input:
integrate(((2*(-3*x^2-6*x)*log(2)-3*x^4)*exp(x)+4*(150*x-30)*log(2)^2+2*(3 00*x^3-60*x^2)*log(2)+150*x^5-30*x^4)/(8*exp(x)^2*x^4+(2*(-400*x^4+160*x^3 -16*x^2)*log(2)-400*x^6+160*x^5-16*x^4)*exp(x)+4*(5000*x^4-4000*x^3+1200*x ^2-160*x+8)*log(2)^2+2*(10000*x^6-8000*x^5+2400*x^4-320*x^3+16*x^2)*log(2) +5000*x^8-4000*x^7+1200*x^6-160*x^5+8*x^4),x, algorithm="fricas")
Output:
-3/8*(x^2 + 2*log(2))/(25*x^4 - 10*x^3 - x^2*e^x + x^2 + 2*(25*x^2 - 10*x + 1)*log(2))
Leaf count of result is larger than twice the leaf count of optimal. 53 vs. \(2 (24) = 48\).
Time = 0.15 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.77 \[ \int \frac {-30 x^4+150 x^5+\left (-60 x^2+300 x^3\right ) \log (4)+(-30+150 x) \log ^2(4)+e^x \left (-3 x^4+\left (-6 x-3 x^2\right ) \log (4)\right )}{8 x^4+8 e^{2 x} x^4-160 x^5+1200 x^6-4000 x^7+5000 x^8+\left (16 x^2-320 x^3+2400 x^4-8000 x^5+10000 x^6\right ) \log (4)+\left (8-160 x+1200 x^2-4000 x^3+5000 x^4\right ) \log ^2(4)+e^x \left (-16 x^4+160 x^5-400 x^6+\left (-16 x^2+160 x^3-400 x^4\right ) \log (4)\right )} \, dx=\frac {3 x^{2} + 6 \log {\left (2 \right )}}{- 200 x^{4} + 80 x^{3} + 8 x^{2} e^{x} - 400 x^{2} \log {\left (2 \right )} - 8 x^{2} + 160 x \log {\left (2 \right )} - 16 \log {\left (2 \right )}} \] Input:
integrate(((2*(-3*x**2-6*x)*ln(2)-3*x**4)*exp(x)+4*(150*x-30)*ln(2)**2+2*( 300*x**3-60*x**2)*ln(2)+150*x**5-30*x**4)/(8*exp(x)**2*x**4+(2*(-400*x**4+ 160*x**3-16*x**2)*ln(2)-400*x**6+160*x**5-16*x**4)*exp(x)+4*(5000*x**4-400 0*x**3+1200*x**2-160*x+8)*ln(2)**2+2*(10000*x**6-8000*x**5+2400*x**4-320*x **3+16*x**2)*ln(2)+5000*x**8-4000*x**7+1200*x**6-160*x**5+8*x**4),x)
Output:
(3*x**2 + 6*log(2))/(-200*x**4 + 80*x**3 + 8*x**2*exp(x) - 400*x**2*log(2) - 8*x**2 + 160*x*log(2) - 16*log(2))
Time = 0.19 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.63 \[ \int \frac {-30 x^4+150 x^5+\left (-60 x^2+300 x^3\right ) \log (4)+(-30+150 x) \log ^2(4)+e^x \left (-3 x^4+\left (-6 x-3 x^2\right ) \log (4)\right )}{8 x^4+8 e^{2 x} x^4-160 x^5+1200 x^6-4000 x^7+5000 x^8+\left (16 x^2-320 x^3+2400 x^4-8000 x^5+10000 x^6\right ) \log (4)+\left (8-160 x+1200 x^2-4000 x^3+5000 x^4\right ) \log ^2(4)+e^x \left (-16 x^4+160 x^5-400 x^6+\left (-16 x^2+160 x^3-400 x^4\right ) \log (4)\right )} \, dx=-\frac {3 \, {\left (x^{2} + 2 \, \log \left (2\right )\right )}}{8 \, {\left (25 \, x^{4} - 10 \, x^{3} + x^{2} {\left (50 \, \log \left (2\right ) + 1\right )} - x^{2} e^{x} - 20 \, x \log \left (2\right ) + 2 \, \log \left (2\right )\right )}} \] Input:
integrate(((2*(-3*x^2-6*x)*log(2)-3*x^4)*exp(x)+4*(150*x-30)*log(2)^2+2*(3 00*x^3-60*x^2)*log(2)+150*x^5-30*x^4)/(8*exp(x)^2*x^4+(2*(-400*x^4+160*x^3 -16*x^2)*log(2)-400*x^6+160*x^5-16*x^4)*exp(x)+4*(5000*x^4-4000*x^3+1200*x ^2-160*x+8)*log(2)^2+2*(10000*x^6-8000*x^5+2400*x^4-320*x^3+16*x^2)*log(2) +5000*x^8-4000*x^7+1200*x^6-160*x^5+8*x^4),x, algorithm="maxima")
Output:
-3/8*(x^2 + 2*log(2))/(25*x^4 - 10*x^3 + x^2*(50*log(2) + 1) - x^2*e^x - 2 0*x*log(2) + 2*log(2))
Time = 0.17 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.63 \[ \int \frac {-30 x^4+150 x^5+\left (-60 x^2+300 x^3\right ) \log (4)+(-30+150 x) \log ^2(4)+e^x \left (-3 x^4+\left (-6 x-3 x^2\right ) \log (4)\right )}{8 x^4+8 e^{2 x} x^4-160 x^5+1200 x^6-4000 x^7+5000 x^8+\left (16 x^2-320 x^3+2400 x^4-8000 x^5+10000 x^6\right ) \log (4)+\left (8-160 x+1200 x^2-4000 x^3+5000 x^4\right ) \log ^2(4)+e^x \left (-16 x^4+160 x^5-400 x^6+\left (-16 x^2+160 x^3-400 x^4\right ) \log (4)\right )} \, dx=-\frac {3 \, {\left (x^{2} + 2 \, \log \left (2\right )\right )}}{8 \, {\left (25 \, x^{4} - 10 \, x^{3} - x^{2} e^{x} + 50 \, x^{2} \log \left (2\right ) + x^{2} - 20 \, x \log \left (2\right ) + 2 \, \log \left (2\right )\right )}} \] Input:
integrate(((2*(-3*x^2-6*x)*log(2)-3*x^4)*exp(x)+4*(150*x-30)*log(2)^2+2*(3 00*x^3-60*x^2)*log(2)+150*x^5-30*x^4)/(8*exp(x)^2*x^4+(2*(-400*x^4+160*x^3 -16*x^2)*log(2)-400*x^6+160*x^5-16*x^4)*exp(x)+4*(5000*x^4-4000*x^3+1200*x ^2-160*x+8)*log(2)^2+2*(10000*x^6-8000*x^5+2400*x^4-320*x^3+16*x^2)*log(2) +5000*x^8-4000*x^7+1200*x^6-160*x^5+8*x^4),x, algorithm="giac")
Output:
-3/8*(x^2 + 2*log(2))/(25*x^4 - 10*x^3 - x^2*e^x + 50*x^2*log(2) + x^2 - 2 0*x*log(2) + 2*log(2))
Timed out. \[ \int \frac {-30 x^4+150 x^5+\left (-60 x^2+300 x^3\right ) \log (4)+(-30+150 x) \log ^2(4)+e^x \left (-3 x^4+\left (-6 x-3 x^2\right ) \log (4)\right )}{8 x^4+8 e^{2 x} x^4-160 x^5+1200 x^6-4000 x^7+5000 x^8+\left (16 x^2-320 x^3+2400 x^4-8000 x^5+10000 x^6\right ) \log (4)+\left (8-160 x+1200 x^2-4000 x^3+5000 x^4\right ) \log ^2(4)+e^x \left (-16 x^4+160 x^5-400 x^6+\left (-16 x^2+160 x^3-400 x^4\right ) \log (4)\right )} \, dx=\int -\frac {{\mathrm {e}}^x\,\left (2\,\ln \left (2\right )\,\left (3\,x^2+6\,x\right )+3\,x^4\right )-4\,{\ln \left (2\right )}^2\,\left (150\,x-30\right )+2\,\ln \left (2\right )\,\left (60\,x^2-300\,x^3\right )+30\,x^4-150\,x^5}{4\,{\ln \left (2\right )}^2\,\left (5000\,x^4-4000\,x^3+1200\,x^2-160\,x+8\right )-{\mathrm {e}}^x\,\left (2\,\ln \left (2\right )\,\left (400\,x^4-160\,x^3+16\,x^2\right )+16\,x^4-160\,x^5+400\,x^6\right )+2\,\ln \left (2\right )\,\left (10000\,x^6-8000\,x^5+2400\,x^4-320\,x^3+16\,x^2\right )+8\,x^4\,{\mathrm {e}}^{2\,x}+8\,x^4-160\,x^5+1200\,x^6-4000\,x^7+5000\,x^8} \,d x \] Input:
int(-(exp(x)*(2*log(2)*(6*x + 3*x^2) + 3*x^4) - 4*log(2)^2*(150*x - 30) + 2*log(2)*(60*x^2 - 300*x^3) + 30*x^4 - 150*x^5)/(4*log(2)^2*(1200*x^2 - 16 0*x - 4000*x^3 + 5000*x^4 + 8) - exp(x)*(2*log(2)*(16*x^2 - 160*x^3 + 400* x^4) + 16*x^4 - 160*x^5 + 400*x^6) + 2*log(2)*(16*x^2 - 320*x^3 + 2400*x^4 - 8000*x^5 + 10000*x^6) + 8*x^4*exp(2*x) + 8*x^4 - 160*x^5 + 1200*x^6 - 4 000*x^7 + 5000*x^8),x)
Output:
int(-(exp(x)*(2*log(2)*(6*x + 3*x^2) + 3*x^4) - 4*log(2)^2*(150*x - 30) + 2*log(2)*(60*x^2 - 300*x^3) + 30*x^4 - 150*x^5)/(4*log(2)^2*(1200*x^2 - 16 0*x - 4000*x^3 + 5000*x^4 + 8) - exp(x)*(2*log(2)*(16*x^2 - 160*x^3 + 400* x^4) + 16*x^4 - 160*x^5 + 400*x^6) + 2*log(2)*(16*x^2 - 320*x^3 + 2400*x^4 - 8000*x^5 + 10000*x^6) + 8*x^4*exp(2*x) + 8*x^4 - 160*x^5 + 1200*x^6 - 4 000*x^7 + 5000*x^8), x)
Time = 0.19 (sec) , antiderivative size = 52, normalized size of antiderivative = 1.73 \[ \int \frac {-30 x^4+150 x^5+\left (-60 x^2+300 x^3\right ) \log (4)+(-30+150 x) \log ^2(4)+e^x \left (-3 x^4+\left (-6 x-3 x^2\right ) \log (4)\right )}{8 x^4+8 e^{2 x} x^4-160 x^5+1200 x^6-4000 x^7+5000 x^8+\left (16 x^2-320 x^3+2400 x^4-8000 x^5+10000 x^6\right ) \log (4)+\left (8-160 x+1200 x^2-4000 x^3+5000 x^4\right ) \log ^2(4)+e^x \left (-16 x^4+160 x^5-400 x^6+\left (-16 x^2+160 x^3-400 x^4\right ) \log (4)\right )} \, dx=\frac {6 \,\mathrm {log}\left (2\right )+3 x^{2}}{8 e^{x} x^{2}-400 \,\mathrm {log}\left (2\right ) x^{2}+160 \,\mathrm {log}\left (2\right ) x -16 \,\mathrm {log}\left (2\right )-200 x^{4}+80 x^{3}-8 x^{2}} \] Input:
int(((2*(-3*x^2-6*x)*log(2)-3*x^4)*exp(x)+4*(150*x-30)*log(2)^2+2*(300*x^3 -60*x^2)*log(2)+150*x^5-30*x^4)/(8*exp(x)^2*x^4+(2*(-400*x^4+160*x^3-16*x^ 2)*log(2)-400*x^6+160*x^5-16*x^4)*exp(x)+4*(5000*x^4-4000*x^3+1200*x^2-160 *x+8)*log(2)^2+2*(10000*x^6-8000*x^5+2400*x^4-320*x^3+16*x^2)*log(2)+5000* x^8-4000*x^7+1200*x^6-160*x^5+8*x^4),x)
Output:
(3*(2*log(2) + x**2))/(8*(e**x*x**2 - 50*log(2)*x**2 + 20*log(2)*x - 2*log (2) - 25*x**4 + 10*x**3 - x**2))