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

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

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Rubi [A]  time = 0.04, antiderivative size = 54, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.040, Rules used = {1657} \begin {gather*} \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 {gather*}

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*}

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Mathematica [A]  time = 0.00, size = 54, normalized size = 1.00 \begin {gather*} \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 {gather*}

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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IntegrateAlgebraic [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \left (3-x+2 x^2\right )^2 \left (2+3 x+5 x^2\right )^2 \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 0.33, size = 44, normalized size = 0.81 \begin {gather*} \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 {gather*}

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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giac [A]  time = 0.20, size = 44, normalized size = 0.81 \begin {gather*} \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 {gather*}

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

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maple [A]  time = 0.00, size = 45, normalized size = 0.83 \begin {gather*} \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 {gather*}

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 = 0.44, size = 44, normalized size = 0.81 \begin {gather*} \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 {gather*}

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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mupad [B]  time = 0.03, size = 44, normalized size = 0.81 \begin {gather*} \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 {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2*x^2 - x + 3)^2*(3*x + 5*x^2 + 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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sympy [A]  time = 0.08, size = 51, normalized size = 0.94 \begin {gather*} \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 {gather*}

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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