3.1828 \(\int \left (a+\frac{b}{x^2}\right )^3 x^6 \, dx\)

Optimal. Leaf size=35 \[ \frac{a^3 x^7}{7}+\frac{3}{5} a^2 b x^5+a b^2 x^3+b^3 x \]

[Out]

b^3*x + a*b^2*x^3 + (3*a^2*b*x^5)/5 + (a^3*x^7)/7

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Rubi [A]  time = 0.0441234, antiderivative size = 35, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{a^3 x^7}{7}+\frac{3}{5} a^2 b x^5+a b^2 x^3+b^3 x \]

Antiderivative was successfully verified.

[In]  Int[(a + b/x^2)^3*x^6,x]

[Out]

b^3*x + a*b^2*x^3 + (3*a^2*b*x^5)/5 + (a^3*x^7)/7

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{a^{3} x^{7}}{7} + \frac{3 a^{2} b x^{5}}{5} + a b^{2} x^{3} + \int b^{3}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((a+b/x**2)**3*x**6,x)

[Out]

a**3*x**7/7 + 3*a**2*b*x**5/5 + a*b**2*x**3 + Integral(b**3, x)

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Mathematica [A]  time = 0.00204309, size = 35, normalized size = 1. \[ \frac{a^3 x^7}{7}+\frac{3}{5} a^2 b x^5+a b^2 x^3+b^3 x \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b/x^2)^3*x^6,x]

[Out]

b^3*x + a*b^2*x^3 + (3*a^2*b*x^5)/5 + (a^3*x^7)/7

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Maple [A]  time = 0.002, size = 32, normalized size = 0.9 \[{b}^{3}x+a{b}^{2}{x}^{3}+{\frac{3\,{a}^{2}b{x}^{5}}{5}}+{\frac{{a}^{3}{x}^{7}}{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((a+b/x^2)^3*x^6,x)

[Out]

b^3*x+a*b^2*x^3+3/5*a^2*b*x^5+1/7*a^3*x^7

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Maxima [A]  time = 1.4482, size = 42, normalized size = 1.2 \[ \frac{1}{7} \, a^{3} x^{7} + \frac{3}{5} \, a^{2} b x^{5} + a b^{2} x^{3} + b^{3} x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a + b/x^2)^3*x^6,x, algorithm="maxima")

[Out]

1/7*a^3*x^7 + 3/5*a^2*b*x^5 + a*b^2*x^3 + b^3*x

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Fricas [A]  time = 0.216728, size = 42, normalized size = 1.2 \[ \frac{1}{7} \, a^{3} x^{7} + \frac{3}{5} \, a^{2} b x^{5} + a b^{2} x^{3} + b^{3} x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a + b/x^2)^3*x^6,x, algorithm="fricas")

[Out]

1/7*a^3*x^7 + 3/5*a^2*b*x^5 + a*b^2*x^3 + b^3*x

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Sympy [A]  time = 0.096353, size = 32, normalized size = 0.91 \[ \frac{a^{3} x^{7}}{7} + \frac{3 a^{2} b x^{5}}{5} + a b^{2} x^{3} + b^{3} x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a+b/x**2)**3*x**6,x)

[Out]

a**3*x**7/7 + 3*a**2*b*x**5/5 + a*b**2*x**3 + b**3*x

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GIAC/XCAS [A]  time = 0.226234, size = 42, normalized size = 1.2 \[ \frac{1}{7} \, a^{3} x^{7} + \frac{3}{5} \, a^{2} b x^{5} + a b^{2} x^{3} + b^{3} x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a + b/x^2)^3*x^6,x, algorithm="giac")

[Out]

1/7*a^3*x^7 + 3/5*a^2*b*x^5 + a*b^2*x^3 + b^3*x