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

Optimal. Leaf size=54 \[ \frac{100 x^9}{9}+\frac{5 x^8}{2}+\frac{321 x^7}{7}+\frac{86 x^6}{3}+78 x^5+59 x^4+\frac{241 x^3}{3}+42 x^2+36 x \]

[Out]

36*x + 42*x^2 + (241*x^3)/3 + 59*x^4 + 78*x^5 + (86*x^6)/3 + (321*x^7)/7 + (5*x^8)/2 + (100*x^9)/9

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Rubi [A]  time = 0.042492, antiderivative size = 54, 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} \[ \frac{100 x^9}{9}+\frac{5 x^8}{2}+\frac{321 x^7}{7}+\frac{86 x^6}{3}+78 x^5+59 x^4+\frac{241 x^3}{3}+42 x^2+36 x \]

Antiderivative was successfully verified.

[In]

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

[Out]

36*x + 42*x^2 + (241*x^3)/3 + 59*x^4 + 78*x^5 + (86*x^6)/3 + (321*x^7)/7 + (5*x^8)/2 + (100*x^9)/9

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 )^2 \, dx &=\int \left (36+84 x+241 x^2+236 x^3+390 x^4+172 x^5+321 x^6+20 x^7+100 x^8\right ) \, dx\\ &=36 x+42 x^2+\frac{241 x^3}{3}+59 x^4+78 x^5+\frac{86 x^6}{3}+\frac{321 x^7}{7}+\frac{5 x^8}{2}+\frac{100 x^9}{9}\\ \end{align*}

Mathematica [A]  time = 0.0017383, size = 54, normalized size = 1. \[ \frac{100 x^9}{9}+\frac{5 x^8}{2}+\frac{321 x^7}{7}+\frac{86 x^6}{3}+78 x^5+59 x^4+\frac{241 x^3}{3}+42 x^2+36 x \]

Antiderivative was successfully verified.

[In]

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

[Out]

36*x + 42*x^2 + (241*x^3)/3 + 59*x^4 + 78*x^5 + (86*x^6)/3 + (321*x^7)/7 + (5*x^8)/2 + (100*x^9)/9

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Maple [A]  time = 0.044, size = 45, normalized size = 0.8 \begin{align*} 36\,x+42\,{x}^{2}+{\frac{241\,{x}^{3}}{3}}+59\,{x}^{4}+78\,{x}^{5}+{\frac{86\,{x}^{6}}{3}}+{\frac{321\,{x}^{7}}{7}}+{\frac{5\,{x}^{8}}{2}}+{\frac{100\,{x}^{9}}{9}} \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)^2,x)

[Out]

36*x+42*x^2+241/3*x^3+59*x^4+78*x^5+86/3*x^6+321/7*x^7+5/2*x^8+100/9*x^9

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Maxima [A]  time = 0.967055, size = 59, normalized size = 1.09 \begin{align*} \frac{100}{9} \, x^{9} + \frac{5}{2} \, x^{8} + \frac{321}{7} \, x^{7} + \frac{86}{3} \, x^{6} + 78 \, x^{5} + 59 \, x^{4} + \frac{241}{3} \, x^{3} + 42 \, x^{2} + 36 \, 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)^2,x, algorithm="maxima")

[Out]

100/9*x^9 + 5/2*x^8 + 321/7*x^7 + 86/3*x^6 + 78*x^5 + 59*x^4 + 241/3*x^3 + 42*x^2 + 36*x

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Fricas [A]  time = 0.904191, size = 122, normalized size = 2.26 \begin{align*} \frac{100}{9} x^{9} + \frac{5}{2} x^{8} + \frac{321}{7} x^{7} + \frac{86}{3} x^{6} + 78 x^{5} + 59 x^{4} + \frac{241}{3} x^{3} + 42 x^{2} + 36 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)^2,x, algorithm="fricas")

[Out]

100/9*x^9 + 5/2*x^8 + 321/7*x^7 + 86/3*x^6 + 78*x^5 + 59*x^4 + 241/3*x^3 + 42*x^2 + 36*x

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Sympy [A]  time = 0.108465, size = 51, normalized size = 0.94 \begin{align*} \frac{100 x^{9}}{9} + \frac{5 x^{8}}{2} + \frac{321 x^{7}}{7} + \frac{86 x^{6}}{3} + 78 x^{5} + 59 x^{4} + \frac{241 x^{3}}{3} + 42 x^{2} + 36 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)**2,x)

[Out]

100*x**9/9 + 5*x**8/2 + 321*x**7/7 + 86*x**6/3 + 78*x**5 + 59*x**4 + 241*x**3/3 + 42*x**2 + 36*x

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Giac [A]  time = 1.19494, size = 59, normalized size = 1.09 \begin{align*} \frac{100}{9} \, x^{9} + \frac{5}{2} \, x^{8} + \frac{321}{7} \, x^{7} + \frac{86}{3} \, x^{6} + 78 \, x^{5} + 59 \, x^{4} + \frac{241}{3} \, x^{3} + 42 \, x^{2} + 36 \, 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)^2,x, algorithm="giac")

[Out]

100/9*x^9 + 5/2*x^8 + 321/7*x^7 + 86/3*x^6 + 78*x^5 + 59*x^4 + 241/3*x^3 + 42*x^2 + 36*x