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

Optimal. Leaf size=68 \[ \frac{200 x^{11}}{11}-6 x^{10}+\frac{922 x^9}{9}+\frac{83 x^8}{8}+\frac{1571 x^7}{7}+\frac{299 x^6}{3}+\frac{1416 x^5}{5}+\frac{635 x^4}{4}+237 x^3+108 x^2+108 x \]

[Out]

108*x + 108*x^2 + 237*x^3 + (635*x^4)/4 + (1416*x^5)/5 + (299*x^6)/3 + (1571*x^7
)/7 + (83*x^8)/8 + (922*x^9)/9 - 6*x^10 + (200*x^11)/11

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Rubi [A]  time = 0.0879937, antiderivative size = 68, 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 \[ \frac{200 x^{11}}{11}-6 x^{10}+\frac{922 x^9}{9}+\frac{83 x^8}{8}+\frac{1571 x^7}{7}+\frac{299 x^6}{3}+\frac{1416 x^5}{5}+\frac{635 x^4}{4}+237 x^3+108 x^2+108 x \]

Antiderivative was successfully verified.

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

[Out]

108*x + 108*x^2 + 237*x^3 + (635*x^4)/4 + (1416*x^5)/5 + (299*x^6)/3 + (1571*x^7
)/7 + (83*x^8)/8 + (922*x^9)/9 - 6*x^10 + (200*x^11)/11

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{3892 x^{9}}{495} - \frac{6387 x^{8}}{440} + \frac{44619 x^{7}}{770} - \frac{89849 x^{6}}{1320} + \frac{61947 x^{5}}{440} - \frac{22329 x^{4}}{220} + \frac{31041 x^{3}}{220} + \frac{28431 x}{440} + \frac{\left (100 x + 107\right ) \left (2 x^{2} - x + 3\right )^{4} \left (5 x^{2} + 3 x + 2\right )}{440} - \frac{21627 \int x\, dx}{220} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

3892*x**9/495 - 6387*x**8/440 + 44619*x**7/770 - 89849*x**6/1320 + 61947*x**5/44
0 - 22329*x**4/220 + 31041*x**3/220 + 28431*x/440 + (100*x + 107)*(2*x**2 - x +
3)**4*(5*x**2 + 3*x + 2)/440 - 21627*Integral(x, x)/220

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Mathematica [A]  time = 0.00366861, size = 68, normalized size = 1. \[ \frac{200 x^{11}}{11}-6 x^{10}+\frac{922 x^9}{9}+\frac{83 x^8}{8}+\frac{1571 x^7}{7}+\frac{299 x^6}{3}+\frac{1416 x^5}{5}+\frac{635 x^4}{4}+237 x^3+108 x^2+108 x \]

Antiderivative was successfully verified.

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

[Out]

108*x + 108*x^2 + 237*x^3 + (635*x^4)/4 + (1416*x^5)/5 + (299*x^6)/3 + (1571*x^7
)/7 + (83*x^8)/8 + (922*x^9)/9 - 6*x^10 + (200*x^11)/11

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Maple [A]  time = 0.002, size = 55, normalized size = 0.8 \[ 108\,x+108\,{x}^{2}+237\,{x}^{3}+{\frac{635\,{x}^{4}}{4}}+{\frac{1416\,{x}^{5}}{5}}+{\frac{299\,{x}^{6}}{3}}+{\frac{1571\,{x}^{7}}{7}}+{\frac{83\,{x}^{8}}{8}}+{\frac{922\,{x}^{9}}{9}}-6\,{x}^{10}+{\frac{200\,{x}^{11}}{11}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

108*x+108*x^2+237*x^3+635/4*x^4+1416/5*x^5+299/3*x^6+1571/7*x^7+83/8*x^8+922/9*x
^9-6*x^10+200/11*x^11

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Maxima [A]  time = 0.688306, size = 73, normalized size = 1.07 \[ \frac{200}{11} \, x^{11} - 6 \, x^{10} + \frac{922}{9} \, x^{9} + \frac{83}{8} \, x^{8} + \frac{1571}{7} \, x^{7} + \frac{299}{3} \, x^{6} + \frac{1416}{5} \, x^{5} + \frac{635}{4} \, x^{4} + 237 \, x^{3} + 108 \, x^{2} + 108 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

200/11*x^11 - 6*x^10 + 922/9*x^9 + 83/8*x^8 + 1571/7*x^7 + 299/3*x^6 + 1416/5*x^
5 + 635/4*x^4 + 237*x^3 + 108*x^2 + 108*x

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Fricas [A]  time = 0.234438, size = 1, normalized size = 0.01 \[ \frac{200}{11} x^{11} - 6 x^{10} + \frac{922}{9} x^{9} + \frac{83}{8} x^{8} + \frac{1571}{7} x^{7} + \frac{299}{3} x^{6} + \frac{1416}{5} x^{5} + \frac{635}{4} x^{4} + 237 x^{3} + 108 x^{2} + 108 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

200/11*x^11 - 6*x^10 + 922/9*x^9 + 83/8*x^8 + 1571/7*x^7 + 299/3*x^6 + 1416/5*x^
5 + 635/4*x^4 + 237*x^3 + 108*x^2 + 108*x

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Sympy [A]  time = 0.068309, size = 65, normalized size = 0.96 \[ \frac{200 x^{11}}{11} - 6 x^{10} + \frac{922 x^{9}}{9} + \frac{83 x^{8}}{8} + \frac{1571 x^{7}}{7} + \frac{299 x^{6}}{3} + \frac{1416 x^{5}}{5} + \frac{635 x^{4}}{4} + 237 x^{3} + 108 x^{2} + 108 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

200*x**11/11 - 6*x**10 + 922*x**9/9 + 83*x**8/8 + 1571*x**7/7 + 299*x**6/3 + 141
6*x**5/5 + 635*x**4/4 + 237*x**3 + 108*x**2 + 108*x

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GIAC/XCAS [A]  time = 0.261301, size = 73, normalized size = 1.07 \[ \frac{200}{11} \, x^{11} - 6 \, x^{10} + \frac{922}{9} \, x^{9} + \frac{83}{8} \, x^{8} + \frac{1571}{7} \, x^{7} + \frac{299}{3} \, x^{6} + \frac{1416}{5} \, x^{5} + \frac{635}{4} \, x^{4} + 237 \, x^{3} + 108 \, x^{2} + 108 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

200/11*x^11 - 6*x^10 + 922/9*x^9 + 83/8*x^8 + 1571/7*x^7 + 299/3*x^6 + 1416/5*x^
5 + 635/4*x^4 + 237*x^3 + 108*x^2 + 108*x