3.23 \(\int \left (3-x+2 x^2\right )^2 \left (2+3 x+5 x^2\right )^3 \, dx\)

Optimal. Leaf size=66 \[ \frac{500 x^{11}}{11}+40 x^{10}+\frac{1865 x^9}{9}+\frac{1863 x^8}{8}+444 x^7+449 x^6+\frac{2693 x^5}{5}+\frac{1615 x^4}{4}+\frac{914 x^3}{3}+138 x^2+72 x \]

[Out]

72*x + 138*x^2 + (914*x^3)/3 + (1615*x^4)/4 + (2693*x^5)/5 + 449*x^6 + 444*x^7 +
(1863*x^8)/8 + (1865*x^9)/9 + 40*x^10 + (500*x^11)/11

_______________________________________________________________________________________

Rubi [A]  time = 0.0810002, antiderivative size = 66, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 25, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.04 \[ \frac{500 x^{11}}{11}+40 x^{10}+\frac{1865 x^9}{9}+\frac{1863 x^8}{8}+444 x^7+449 x^6+\frac{2693 x^5}{5}+\frac{1615 x^4}{4}+\frac{914 x^3}{3}+138 x^2+72 x \]

Antiderivative was successfully verified.

[In]  Int[(3 - x + 2*x^2)^2*(2 + 3*x + 5*x^2)^3,x]

[Out]

72*x + 138*x^2 + (914*x^3)/3 + (1615*x^4)/4 + (2693*x^5)/5 + 449*x^6 + 444*x^7 +
(1863*x^8)/8 + (1865*x^9)/9 + 40*x^10 + (500*x^11)/11

_______________________________________________________________________________________

Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{1363 x^{9}}{99} - \frac{14631 x^{8}}{440} + \frac{14233 x^{7}}{220} - \frac{23809 x^{6}}{220} + \frac{1241 x^{5}}{22} - \frac{26469 x^{4}}{220} - \frac{3593 x^{3}}{132} - \frac{576 x}{55} + \frac{\left (100 x + 118\right ) \left (2 x^{2} - x + 3\right )^{3} \left (5 x^{2} + 3 x + 2\right )^{2}}{440} - \frac{22389 \int x\, dx}{110} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((2*x**2-x+3)**2*(5*x**2+3*x+2)**3,x)

[Out]

1363*x**9/99 - 14631*x**8/440 + 14233*x**7/220 - 23809*x**6/220 + 1241*x**5/22 -
26469*x**4/220 - 3593*x**3/132 - 576*x/55 + (100*x + 118)*(2*x**2 - x + 3)**3*(
5*x**2 + 3*x + 2)**2/440 - 22389*Integral(x, x)/110

_______________________________________________________________________________________

Mathematica [A]  time = 0.00485606, size = 66, normalized size = 1. \[ \frac{500 x^{11}}{11}+40 x^{10}+\frac{1865 x^9}{9}+\frac{1863 x^8}{8}+444 x^7+449 x^6+\frac{2693 x^5}{5}+\frac{1615 x^4}{4}+\frac{914 x^3}{3}+138 x^2+72 x \]

Antiderivative was successfully verified.

[In]  Integrate[(3 - x + 2*x^2)^2*(2 + 3*x + 5*x^2)^3,x]

[Out]

72*x + 138*x^2 + (914*x^3)/3 + (1615*x^4)/4 + (2693*x^5)/5 + 449*x^6 + 444*x^7 +
(1863*x^8)/8 + (1865*x^9)/9 + 40*x^10 + (500*x^11)/11

_______________________________________________________________________________________

Maple [A]  time = 0.002, size = 55, normalized size = 0.8 \[ 72\,x+138\,{x}^{2}+{\frac{914\,{x}^{3}}{3}}+{\frac{1615\,{x}^{4}}{4}}+{\frac{2693\,{x}^{5}}{5}}+449\,{x}^{6}+444\,{x}^{7}+{\frac{1863\,{x}^{8}}{8}}+{\frac{1865\,{x}^{9}}{9}}+40\,{x}^{10}+{\frac{500\,{x}^{11}}{11}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((2*x^2-x+3)^2*(5*x^2+3*x+2)^3,x)

[Out]

72*x+138*x^2+914/3*x^3+1615/4*x^4+2693/5*x^5+449*x^6+444*x^7+1863/8*x^8+1865/9*x
^9+40*x^10+500/11*x^11

_______________________________________________________________________________________

Maxima [A]  time = 0.69438, size = 73, normalized size = 1.11 \[ \frac{500}{11} \, x^{11} + 40 \, x^{10} + \frac{1865}{9} \, x^{9} + \frac{1863}{8} \, x^{8} + 444 \, x^{7} + 449 \, x^{6} + \frac{2693}{5} \, x^{5} + \frac{1615}{4} \, x^{4} + \frac{914}{3} \, x^{3} + 138 \, x^{2} + 72 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x^2 + 3*x + 2)^3*(2*x^2 - x + 3)^2,x, algorithm="maxima")

[Out]

500/11*x^11 + 40*x^10 + 1865/9*x^9 + 1863/8*x^8 + 444*x^7 + 449*x^6 + 2693/5*x^5
+ 1615/4*x^4 + 914/3*x^3 + 138*x^2 + 72*x

_______________________________________________________________________________________

Fricas [A]  time = 0.230541, size = 1, normalized size = 0.02 \[ \frac{500}{11} x^{11} + 40 x^{10} + \frac{1865}{9} x^{9} + \frac{1863}{8} x^{8} + 444 x^{7} + 449 x^{6} + \frac{2693}{5} x^{5} + \frac{1615}{4} x^{4} + \frac{914}{3} x^{3} + 138 x^{2} + 72 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x^2 + 3*x + 2)^3*(2*x^2 - x + 3)^2,x, algorithm="fricas")

[Out]

500/11*x^11 + 40*x^10 + 1865/9*x^9 + 1863/8*x^8 + 444*x^7 + 449*x^6 + 2693/5*x^5
+ 1615/4*x^4 + 914/3*x^3 + 138*x^2 + 72*x

_______________________________________________________________________________________

Sympy [A]  time = 0.07288, size = 63, normalized size = 0.95 \[ \frac{500 x^{11}}{11} + 40 x^{10} + \frac{1865 x^{9}}{9} + \frac{1863 x^{8}}{8} + 444 x^{7} + 449 x^{6} + \frac{2693 x^{5}}{5} + \frac{1615 x^{4}}{4} + \frac{914 x^{3}}{3} + 138 x^{2} + 72 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2*x**2-x+3)**2*(5*x**2+3*x+2)**3,x)

[Out]

500*x**11/11 + 40*x**10 + 1865*x**9/9 + 1863*x**8/8 + 444*x**7 + 449*x**6 + 2693
*x**5/5 + 1615*x**4/4 + 914*x**3/3 + 138*x**2 + 72*x

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.262148, size = 73, normalized size = 1.11 \[ \frac{500}{11} \, x^{11} + 40 \, x^{10} + \frac{1865}{9} \, x^{9} + \frac{1863}{8} \, x^{8} + 444 \, x^{7} + 449 \, x^{6} + \frac{2693}{5} \, x^{5} + \frac{1615}{4} \, x^{4} + \frac{914}{3} \, x^{3} + 138 \, x^{2} + 72 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x^2 + 3*x + 2)^3*(2*x^2 - x + 3)^2,x, algorithm="giac")

[Out]

500/11*x^11 + 40*x^10 + 1865/9*x^9 + 1863/8*x^8 + 444*x^7 + 449*x^6 + 2693/5*x^5
+ 1615/4*x^4 + 914/3*x^3 + 138*x^2 + 72*x