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

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 + (27763*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 = 0.0599792, 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, Rules used = {1657} \[ \frac{2500 x^{13}}{13}+\frac{875 x^{12}}{3}+\frac{11525 x^{11}}{11}+1571 x^{10}+\frac{24859 x^9}{9}+3315 x^8+\frac{27763 x^7}{7}+\frac{10771 x^6}{3}+\frac{14801 x^5}{5}+1838 x^4+\frac{3016 x^3}{3}+384 x^2+144 x \]

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 + (27763*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

Rule 1657

Int[(Pq_)*((a_) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_.), x_Symbol] :> Int[ExpandIntegrand[Pq*(a + b*x + c*x^2)^p, x
], x] /; FreeQ[{a, b, c}, x] && PolyQ[Pq, x] && IGtQ[p, -2]

Rubi steps

\begin{align*} \int \left (3-x+2 x^2\right )^2 \left (2+3 x+5 x^2\right )^4 \, dx &=\int \left (144+768 x+3016 x^2+7352 x^3+14801 x^4+21542 x^5+27763 x^6+26520 x^7+24859 x^8+15710 x^9+11525 x^{10}+3500 x^{11}+2500 x^{12}\right ) \, dx\\ &=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}\\ \end{align*}

Mathematica [A]  time = 0.0029768, 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 + (27763*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 = 0.043, size = 65, normalized size = 0.8 \begin{align*} 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}} \end{align*}

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+24859/9*x^9+1571*x^10+11525/11*
x^11+875/3*x^12+2500/13*x^13

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Maxima [A]  time = 0.956925, size = 86, normalized size = 1.08 \begin{align*} \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 \end{align*}

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, 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 + 1
4801/5*x^5 + 1838*x^4 + 3016/3*x^3 + 384*x^2 + 144*x

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Fricas [A]  time = 0.62232, size = 221, normalized size = 2.76 \begin{align*} \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 \end{align*}

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, 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 + 1
4801/5*x^5 + 1838*x^4 + 3016/3*x^3 + 384*x^2 + 144*x

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Sympy [A]  time = 0.133479, size = 76, normalized size = 0.95 \begin{align*} \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 \end{align*}

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 + 384*x**2 + 144*x

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Giac [A]  time = 1.19878, size = 86, normalized size = 1.08 \begin{align*} \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 \end{align*}

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, 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 + 1
4801/5*x^5 + 1838*x^4 + 3016/3*x^3 + 384*x^2 + 144*x