3.59 \(\int (8+24 x+8 x^2-15 x^3+8 x^4)^2 \, dx\)

Optimal. Leaf size=52 \[ \frac{64 x^9}{9}-30 x^8+\frac{353 x^7}{7}+24 x^6-\frac{528 x^5}{5}+36 x^4+\frac{704 x^3}{3}+192 x^2+64 x \]

[Out]

64*x + 192*x^2 + (704*x^3)/3 + 36*x^4 - (528*x^5)/5 + 24*x^6 + (353*x^7)/7 - 30*x^8 + (64*x^9)/9

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Rubi [A]  time = 0.0160692, antiderivative size = 52, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045, Rules used = {2061} \[ \frac{64 x^9}{9}-30 x^8+\frac{353 x^7}{7}+24 x^6-\frac{528 x^5}{5}+36 x^4+\frac{704 x^3}{3}+192 x^2+64 x \]

Antiderivative was successfully verified.

[In]

Int[(8 + 24*x + 8*x^2 - 15*x^3 + 8*x^4)^2,x]

[Out]

64*x + 192*x^2 + (704*x^3)/3 + 36*x^4 - (528*x^5)/5 + 24*x^6 + (353*x^7)/7 - 30*x^8 + (64*x^9)/9

Rule 2061

Int[(P_)^(p_), x_Symbol] :> Int[ExpandToSum[P^p, x], x] /; PolyQ[P, x] && IGtQ[p, 0]

Rubi steps

\begin{align*} \int \left (8+24 x+8 x^2-15 x^3+8 x^4\right )^2 \, dx &=\int \left (64+384 x+704 x^2+144 x^3-528 x^4+144 x^5+353 x^6-240 x^7+64 x^8\right ) \, dx\\ &=64 x+192 x^2+\frac{704 x^3}{3}+36 x^4-\frac{528 x^5}{5}+24 x^6+\frac{353 x^7}{7}-30 x^8+\frac{64 x^9}{9}\\ \end{align*}

Mathematica [A]  time = 0.0014015, size = 52, normalized size = 1. \[ \frac{64 x^9}{9}-30 x^8+\frac{353 x^7}{7}+24 x^6-\frac{528 x^5}{5}+36 x^4+\frac{704 x^3}{3}+192 x^2+64 x \]

Antiderivative was successfully verified.

[In]

Integrate[(8 + 24*x + 8*x^2 - 15*x^3 + 8*x^4)^2,x]

[Out]

64*x + 192*x^2 + (704*x^3)/3 + 36*x^4 - (528*x^5)/5 + 24*x^6 + (353*x^7)/7 - 30*x^8 + (64*x^9)/9

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Maple [A]  time = 0., size = 45, normalized size = 0.9 \begin{align*} 64\,x+192\,{x}^{2}+{\frac{704\,{x}^{3}}{3}}+36\,{x}^{4}-{\frac{528\,{x}^{5}}{5}}+24\,{x}^{6}+{\frac{353\,{x}^{7}}{7}}-30\,{x}^{8}+{\frac{64\,{x}^{9}}{9}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((8*x^4-15*x^3+8*x^2+24*x+8)^2,x)

[Out]

64*x+192*x^2+704/3*x^3+36*x^4-528/5*x^5+24*x^6+353/7*x^7-30*x^8+64/9*x^9

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Maxima [A]  time = 1.33984, size = 59, normalized size = 1.13 \begin{align*} \frac{64}{9} \, x^{9} - 30 \, x^{8} + \frac{353}{7} \, x^{7} + 24 \, x^{6} - \frac{528}{5} \, x^{5} + 36 \, x^{4} + \frac{704}{3} \, x^{3} + 192 \, x^{2} + 64 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((8*x^4-15*x^3+8*x^2+24*x+8)^2,x, algorithm="maxima")

[Out]

64/9*x^9 - 30*x^8 + 353/7*x^7 + 24*x^6 - 528/5*x^5 + 36*x^4 + 704/3*x^3 + 192*x^2 + 64*x

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Fricas [A]  time = 1.33198, size = 122, normalized size = 2.35 \begin{align*} \frac{64}{9} x^{9} - 30 x^{8} + \frac{353}{7} x^{7} + 24 x^{6} - \frac{528}{5} x^{5} + 36 x^{4} + \frac{704}{3} x^{3} + 192 x^{2} + 64 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((8*x^4-15*x^3+8*x^2+24*x+8)^2,x, algorithm="fricas")

[Out]

64/9*x^9 - 30*x^8 + 353/7*x^7 + 24*x^6 - 528/5*x^5 + 36*x^4 + 704/3*x^3 + 192*x^2 + 64*x

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Sympy [A]  time = 0.06325, size = 49, normalized size = 0.94 \begin{align*} \frac{64 x^{9}}{9} - 30 x^{8} + \frac{353 x^{7}}{7} + 24 x^{6} - \frac{528 x^{5}}{5} + 36 x^{4} + \frac{704 x^{3}}{3} + 192 x^{2} + 64 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((8*x**4-15*x**3+8*x**2+24*x+8)**2,x)

[Out]

64*x**9/9 - 30*x**8 + 353*x**7/7 + 24*x**6 - 528*x**5/5 + 36*x**4 + 704*x**3/3 + 192*x**2 + 64*x

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Giac [A]  time = 1.11621, size = 59, normalized size = 1.13 \begin{align*} \frac{64}{9} \, x^{9} - 30 \, x^{8} + \frac{353}{7} \, x^{7} + 24 \, x^{6} - \frac{528}{5} \, x^{5} + 36 \, x^{4} + \frac{704}{3} \, x^{3} + 192 \, x^{2} + 64 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((8*x^4-15*x^3+8*x^2+24*x+8)^2,x, algorithm="giac")

[Out]

64/9*x^9 - 30*x^8 + 353/7*x^7 + 24*x^6 - 528/5*x^5 + 36*x^4 + 704/3*x^3 + 192*x^2 + 64*x