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

Optimal. Leaf size=46 \[ \frac{20 x^7}{7}-\frac{4 x^6}{3}+\frac{61 x^5}{5}+\frac{x^4}{4}+\frac{53 x^3}{3}+\frac{15 x^2}{2}+18 x \]

[Out]

18*x + (15*x^2)/2 + (53*x^3)/3 + x^4/4 + (61*x^5)/5 - (4*x^6)/3 + (20*x^7)/7

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Rubi [A]  time = 0.0470669, antiderivative size = 46, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 23, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.043 \[ \frac{20 x^7}{7}-\frac{4 x^6}{3}+\frac{61 x^5}{5}+\frac{x^4}{4}+\frac{53 x^3}{3}+\frac{15 x^2}{2}+18 x \]

Antiderivative was successfully verified.

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

[Out]

18*x + (15*x^2)/2 + (53*x^3)/3 + x^4/4 + (61*x^5)/5 - (4*x^6)/3 + (20*x^7)/7

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{20 x^{7}}{7} - \frac{4 x^{6}}{3} + \frac{61 x^{5}}{5} + \frac{x^{4}}{4} + \frac{53 x^{3}}{3} + 18 x + 15 \int x\, dx \]

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),x)

[Out]

20*x**7/7 - 4*x**6/3 + 61*x**5/5 + x**4/4 + 53*x**3/3 + 18*x + 15*Integral(x, x)

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Mathematica [A]  time = 0.00256626, size = 46, normalized size = 1. \[ \frac{20 x^7}{7}-\frac{4 x^6}{3}+\frac{61 x^5}{5}+\frac{x^4}{4}+\frac{53 x^3}{3}+\frac{15 x^2}{2}+18 x \]

Antiderivative was successfully verified.

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

[Out]

18*x + (15*x^2)/2 + (53*x^3)/3 + x^4/4 + (61*x^5)/5 - (4*x^6)/3 + (20*x^7)/7

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Maple [A]  time = 0.001, size = 35, normalized size = 0.8 \[ 18\,x+{\frac{15\,{x}^{2}}{2}}+{\frac{53\,{x}^{3}}{3}}+{\frac{{x}^{4}}{4}}+{\frac{61\,{x}^{5}}{5}}-{\frac{4\,{x}^{6}}{3}}+{\frac{20\,{x}^{7}}{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

18*x+15/2*x^2+53/3*x^3+1/4*x^4+61/5*x^5-4/3*x^6+20/7*x^7

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Maxima [A]  time = 0.699221, size = 46, normalized size = 1. \[ \frac{20}{7} \, x^{7} - \frac{4}{3} \, x^{6} + \frac{61}{5} \, x^{5} + \frac{1}{4} \, x^{4} + \frac{53}{3} \, x^{3} + \frac{15}{2} \, x^{2} + 18 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

20/7*x^7 - 4/3*x^6 + 61/5*x^5 + 1/4*x^4 + 53/3*x^3 + 15/2*x^2 + 18*x

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Fricas [A]  time = 0.234106, size = 1, normalized size = 0.02 \[ \frac{20}{7} x^{7} - \frac{4}{3} x^{6} + \frac{61}{5} x^{5} + \frac{1}{4} x^{4} + \frac{53}{3} x^{3} + \frac{15}{2} x^{2} + 18 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

20/7*x^7 - 4/3*x^6 + 61/5*x^5 + 1/4*x^4 + 53/3*x^3 + 15/2*x^2 + 18*x

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Sympy [A]  time = 0.054093, size = 41, normalized size = 0.89 \[ \frac{20 x^{7}}{7} - \frac{4 x^{6}}{3} + \frac{61 x^{5}}{5} + \frac{x^{4}}{4} + \frac{53 x^{3}}{3} + \frac{15 x^{2}}{2} + 18 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

20*x**7/7 - 4*x**6/3 + 61*x**5/5 + x**4/4 + 53*x**3/3 + 15*x**2/2 + 18*x

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GIAC/XCAS [A]  time = 0.263107, size = 46, normalized size = 1. \[ \frac{20}{7} \, x^{7} - \frac{4}{3} \, x^{6} + \frac{61}{5} \, x^{5} + \frac{1}{4} \, x^{4} + \frac{53}{3} \, x^{3} + \frac{15}{2} \, x^{2} + 18 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

20/7*x^7 - 4/3*x^6 + 61/5*x^5 + 1/4*x^4 + 53/3*x^3 + 15/2*x^2 + 18*x