3.22 \(\int \left (3-x+2 x^2\right )^2 \left (2+3 x+5 x^2\right )^4 \, dx\)

Optimal. Leaf size=80 \[ \frac{2500 x^{13}}{13}+\frac{875 x^{12}}{3}+\frac{11525 x^{11}}{11}+1571 x^{10}+\frac{24859 x^9}{9}+3315 x^8+\frac{27763 x^7}{7}+\frac{10771 x^6}{3}+\frac{14801 x^5}{5}+1838 x^4+\frac{3016 x^3}{3}+384 x^2+144 x \]

[Out]

144*x + 384*x^2 + (3016*x^3)/3 + 1838*x^4 + (14801*x^5)/5 + (10771*x^6)/3 + (277
63*x^7)/7 + 3315*x^8 + (24859*x^9)/9 + 1571*x^10 + (11525*x^11)/11 + (875*x^12)/
3 + (2500*x^13)/13

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Rubi [A]  time = 0.0975811, antiderivative size = 80, 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 \[ \frac{2500 x^{13}}{13}+\frac{875 x^{12}}{3}+\frac{11525 x^{11}}{11}+1571 x^{10}+\frac{24859 x^9}{9}+3315 x^8+\frac{27763 x^7}{7}+\frac{10771 x^6}{3}+\frac{14801 x^5}{5}+1838 x^4+\frac{3016 x^3}{3}+384 x^2+144 x \]

Antiderivative was successfully verified.

[In]  Int[(3 - x + 2*x^2)^2*(2 + 3*x + 5*x^2)^4,x]

[Out]

144*x + 384*x^2 + (3016*x^3)/3 + 1838*x^4 + (14801*x^5)/5 + (10771*x^6)/3 + (277
63*x^7)/7 + 3315*x^8 + (24859*x^9)/9 + 1571*x^10 + (11525*x^11)/11 + (875*x^12)/
3 + (2500*x^13)/13

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{13925 x^{11}}{286} - \frac{591 x^{10}}{4} + \frac{124337 x^{9}}{936} - \frac{6836 x^{8}}{13} - \frac{135241 x^{7}}{728} - \frac{68531 x^{6}}{78} - \frac{338541 x^{5}}{520} - \frac{12535 x^{4}}{13} - \frac{170195 x^{3}}{312} - \frac{1935 x}{26} + \frac{\left (120 x + 146\right ) \left (2 x^{2} - x + 3\right )^{3} \left (5 x^{2} + 3 x + 2\right )^{3}}{624} - \frac{19347 \int x\, dx}{26} \]

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)**4,x)

[Out]

13925*x**11/286 - 591*x**10/4 + 124337*x**9/936 - 6836*x**8/13 - 135241*x**7/728
- 68531*x**6/78 - 338541*x**5/520 - 12535*x**4/13 - 170195*x**3/312 - 1935*x/26
+ (120*x + 146)*(2*x**2 - x + 3)**3*(5*x**2 + 3*x + 2)**3/624 - 19347*Integral(
x, x)/26

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Mathematica [A]  time = 0.00526244, size = 80, normalized size = 1. \[ \frac{2500 x^{13}}{13}+\frac{875 x^{12}}{3}+\frac{11525 x^{11}}{11}+1571 x^{10}+\frac{24859 x^9}{9}+3315 x^8+\frac{27763 x^7}{7}+\frac{10771 x^6}{3}+\frac{14801 x^5}{5}+1838 x^4+\frac{3016 x^3}{3}+384 x^2+144 x \]

Antiderivative was successfully verified.

[In]  Integrate[(3 - x + 2*x^2)^2*(2 + 3*x + 5*x^2)^4,x]

[Out]

144*x + 384*x^2 + (3016*x^3)/3 + 1838*x^4 + (14801*x^5)/5 + (10771*x^6)/3 + (277
63*x^7)/7 + 3315*x^8 + (24859*x^9)/9 + 1571*x^10 + (11525*x^11)/11 + (875*x^12)/
3 + (2500*x^13)/13

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Maple [A]  time = 0.002, size = 65, normalized size = 0.8 \[ 144\,x+384\,{x}^{2}+{\frac{3016\,{x}^{3}}{3}}+1838\,{x}^{4}+{\frac{14801\,{x}^{5}}{5}}+{\frac{10771\,{x}^{6}}{3}}+{\frac{27763\,{x}^{7}}{7}}+3315\,{x}^{8}+{\frac{24859\,{x}^{9}}{9}}+1571\,{x}^{10}+{\frac{11525\,{x}^{11}}{11}}+{\frac{875\,{x}^{12}}{3}}+{\frac{2500\,{x}^{13}}{13}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((2*x^2-x+3)^2*(5*x^2+3*x+2)^4,x)

[Out]

144*x+384*x^2+3016/3*x^3+1838*x^4+14801/5*x^5+10771/3*x^6+27763/7*x^7+3315*x^8+2
4859/9*x^9+1571*x^10+11525/11*x^11+875/3*x^12+2500/13*x^13

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Maxima [A]  time = 0.696833, size = 86, normalized size = 1.08 \[ \frac{2500}{13} \, x^{13} + \frac{875}{3} \, x^{12} + \frac{11525}{11} \, x^{11} + 1571 \, x^{10} + \frac{24859}{9} \, x^{9} + 3315 \, x^{8} + \frac{27763}{7} \, x^{7} + \frac{10771}{3} \, x^{6} + \frac{14801}{5} \, x^{5} + 1838 \, x^{4} + \frac{3016}{3} \, x^{3} + 384 \, x^{2} + 144 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x^2 + 3*x + 2)^4*(2*x^2 - x + 3)^2,x, algorithm="maxima")

[Out]

2500/13*x^13 + 875/3*x^12 + 11525/11*x^11 + 1571*x^10 + 24859/9*x^9 + 3315*x^8 +
27763/7*x^7 + 10771/3*x^6 + 14801/5*x^5 + 1838*x^4 + 3016/3*x^3 + 384*x^2 + 144
*x

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Fricas [A]  time = 0.25058, size = 1, normalized size = 0.01 \[ \frac{2500}{13} x^{13} + \frac{875}{3} x^{12} + \frac{11525}{11} x^{11} + 1571 x^{10} + \frac{24859}{9} x^{9} + 3315 x^{8} + \frac{27763}{7} x^{7} + \frac{10771}{3} x^{6} + \frac{14801}{5} x^{5} + 1838 x^{4} + \frac{3016}{3} x^{3} + 384 x^{2} + 144 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x^2 + 3*x + 2)^4*(2*x^2 - x + 3)^2,x, algorithm="fricas")

[Out]

2500/13*x^13 + 875/3*x^12 + 11525/11*x^11 + 1571*x^10 + 24859/9*x^9 + 3315*x^8 +
27763/7*x^7 + 10771/3*x^6 + 14801/5*x^5 + 1838*x^4 + 3016/3*x^3 + 384*x^2 + 144
*x

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Sympy [A]  time = 0.07978, size = 76, normalized size = 0.95 \[ \frac{2500 x^{13}}{13} + \frac{875 x^{12}}{3} + \frac{11525 x^{11}}{11} + 1571 x^{10} + \frac{24859 x^{9}}{9} + 3315 x^{8} + \frac{27763 x^{7}}{7} + \frac{10771 x^{6}}{3} + \frac{14801 x^{5}}{5} + 1838 x^{4} + \frac{3016 x^{3}}{3} + 384 x^{2} + 144 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2*x**2-x+3)**2*(5*x**2+3*x+2)**4,x)

[Out]

2500*x**13/13 + 875*x**12/3 + 11525*x**11/11 + 1571*x**10 + 24859*x**9/9 + 3315*
x**8 + 27763*x**7/7 + 10771*x**6/3 + 14801*x**5/5 + 1838*x**4 + 3016*x**3/3 + 38
4*x**2 + 144*x

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GIAC/XCAS [A]  time = 0.263289, size = 86, normalized size = 1.08 \[ \frac{2500}{13} \, x^{13} + \frac{875}{3} \, x^{12} + \frac{11525}{11} \, x^{11} + 1571 \, x^{10} + \frac{24859}{9} \, x^{9} + 3315 \, x^{8} + \frac{27763}{7} \, x^{7} + \frac{10771}{3} \, x^{6} + \frac{14801}{5} \, x^{5} + 1838 \, x^{4} + \frac{3016}{3} \, x^{3} + 384 \, x^{2} + 144 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x^2 + 3*x + 2)^4*(2*x^2 - x + 3)^2,x, algorithm="giac")

[Out]

2500/13*x^13 + 875/3*x^12 + 11525/11*x^11 + 1571*x^10 + 24859/9*x^9 + 3315*x^8 +
27763/7*x^7 + 10771/3*x^6 + 14801/5*x^5 + 1838*x^4 + 3016/3*x^3 + 384*x^2 + 144
*x