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

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 = 0.0505835, 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, Rules used = {1657} \[ \frac{200 x^{11}}{11}-6 x^{10}+\frac{922 x^9}{9}+\frac{83 x^8}{8}+\frac{1571 x^7}{7}+\frac{299 x^6}{3}+\frac{1416 x^5}{5}+\frac{635 x^4}{4}+237 x^3+108 x^2+108 x \]

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

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 )^3 \left (2+3 x+5 x^2\right )^2 \, dx &=\int \left (108+216 x+711 x^2+635 x^3+1416 x^4+598 x^5+1571 x^6+83 x^7+922 x^8-60 x^9+200 x^{10}\right ) \, dx\\ &=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}\\ \end{align*}

Mathematica [A]  time = 0.0022274, 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 = 0.043, size = 55, normalized size = 0.8 \begin{align*} 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}} \end{align*}

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 = 0.956996, size = 73, normalized size = 1.07 \begin{align*} \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 \end{align*}

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, 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 = 0.850299, size = 166, normalized size = 2.44 \begin{align*} \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 \end{align*}

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, 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 = 0.085544, size = 65, normalized size = 0.96 \begin{align*} \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 \end{align*}

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 + 1416*x**5/5 + 635*x**4/4 + 237*x*
*3 + 108*x**2 + 108*x

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Giac [A]  time = 1.19404, size = 73, normalized size = 1.07 \begin{align*} \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 \end{align*}

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, 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