3.341 \(\int x \left (5+x^2\right )^8 \, dx\)

Optimal. Leaf size=11 \[ \frac{1}{18} \left (x^2+5\right )^9 \]

[Out]

(5 + x^2)^9/18

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Rubi [A]  time = 0.00692123, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ \frac{1}{18} \left (x^2+5\right )^9 \]

Antiderivative was successfully verified.

[In]  Int[x*(5 + x^2)^8,x]

[Out]

(5 + x^2)^9/18

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Rubi in Sympy [A]  time = 0.778112, size = 7, normalized size = 0.64 \[ \frac{\left (x^{2} + 5\right )^{9}}{18} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x*(x**2+5)**8,x)

[Out]

(x**2 + 5)**9/18

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Mathematica [A]  time = 0.0026133, size = 11, normalized size = 1. \[ \frac{1}{18} \left (x^2+5\right )^9 \]

Antiderivative was successfully verified.

[In]  Integrate[x*(5 + x^2)^8,x]

[Out]

(5 + x^2)^9/18

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Maple [B]  time = 0.003, size = 47, normalized size = 4.3 \[{\frac{{x}^{18}}{18}}+{\frac{5\,{x}^{16}}{2}}+50\,{x}^{14}+{\frac{1750\,{x}^{12}}{3}}+4375\,{x}^{10}+21875\,{x}^{8}+{\frac{218750\,{x}^{6}}{3}}+156250\,{x}^{4}+{\frac{390625\,{x}^{2}}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x*(x^2+5)^8,x)

[Out]

1/18*x^18+5/2*x^16+50*x^14+1750/3*x^12+4375*x^10+21875*x^8+218750/3*x^6+156250*x
^4+390625/2*x^2

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Maxima [A]  time = 1.35063, size = 12, normalized size = 1.09 \[ \frac{1}{18} \,{\left (x^{2} + 5\right )}^{9} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^2 + 5)^8*x,x, algorithm="maxima")

[Out]

1/18*(x^2 + 5)^9

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Fricas [A]  time = 0.167509, size = 1, normalized size = 0.09 \[ \frac{1}{18} x^{18} + \frac{5}{2} x^{16} + 50 x^{14} + \frac{1750}{3} x^{12} + 4375 x^{10} + 21875 x^{8} + \frac{218750}{3} x^{6} + 156250 x^{4} + \frac{390625}{2} x^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^2 + 5)^8*x,x, algorithm="fricas")

[Out]

1/18*x^18 + 5/2*x^16 + 50*x^14 + 1750/3*x^12 + 4375*x^10 + 21875*x^8 + 218750/3*
x^6 + 156250*x^4 + 390625/2*x^2

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Sympy [A]  time = 0.038304, size = 51, normalized size = 4.64 \[ \frac{x^{18}}{18} + \frac{5 x^{16}}{2} + 50 x^{14} + \frac{1750 x^{12}}{3} + 4375 x^{10} + 21875 x^{8} + \frac{218750 x^{6}}{3} + 156250 x^{4} + \frac{390625 x^{2}}{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x*(x**2+5)**8,x)

[Out]

x**18/18 + 5*x**16/2 + 50*x**14 + 1750*x**12/3 + 4375*x**10 + 21875*x**8 + 21875
0*x**6/3 + 156250*x**4 + 390625*x**2/2

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GIAC/XCAS [A]  time = 0.209293, size = 12, normalized size = 1.09 \[ \frac{1}{18} \,{\left (x^{2} + 5\right )}^{9} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^2 + 5)^8*x,x, algorithm="giac")

[Out]

1/18*(x^2 + 5)^9