3.1804 \(\int \left (a+\frac{b}{x^2}\right ) x^4 \, dx\)

Optimal. Leaf size=17 \[ \frac{a x^5}{5}+\frac{b x^3}{3} \]

[Out]

(b*x^3)/3 + (a*x^5)/5

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Rubi [A]  time = 0.015812, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{a x^5}{5}+\frac{b x^3}{3} \]

Antiderivative was successfully verified.

[In]  Int[(a + b/x^2)*x^4,x]

[Out]

(b*x^3)/3 + (a*x^5)/5

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Rubi in Sympy [A]  time = 2.77901, size = 12, normalized size = 0.71 \[ \frac{a x^{5}}{5} + \frac{b x^{3}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((a+b/x**2)*x**4,x)

[Out]

a*x**5/5 + b*x**3/3

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Mathematica [A]  time = 0.00210709, size = 17, normalized size = 1. \[ \frac{a x^5}{5}+\frac{b x^3}{3} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b/x^2)*x^4,x]

[Out]

(b*x^3)/3 + (a*x^5)/5

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Maple [A]  time = 0.001, size = 14, normalized size = 0.8 \[{\frac{b{x}^{3}}{3}}+{\frac{a{x}^{5}}{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((a+b/x^2)*x^4,x)

[Out]

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

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Maxima [A]  time = 1.43008, size = 18, normalized size = 1.06 \[ \frac{1}{5} \, a x^{5} + \frac{1}{3} \, b x^{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a + b/x^2)*x^4,x, algorithm="maxima")

[Out]

1/5*a*x^5 + 1/3*b*x^3

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Fricas [A]  time = 0.223325, size = 18, normalized size = 1.06 \[ \frac{1}{5} \, a x^{5} + \frac{1}{3} \, b x^{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a + b/x^2)*x^4,x, algorithm="fricas")

[Out]

1/5*a*x^5 + 1/3*b*x^3

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Sympy [A]  time = 0.065885, size = 12, normalized size = 0.71 \[ \frac{a x^{5}}{5} + \frac{b x^{3}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a+b/x**2)*x**4,x)

[Out]

a*x**5/5 + b*x**3/3

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GIAC/XCAS [A]  time = 0.228078, size = 18, normalized size = 1.06 \[ \frac{1}{5} \, a x^{5} + \frac{1}{3} \, b x^{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a + b/x^2)*x^4,x, algorithm="giac")

[Out]

1/5*a*x^5 + 1/3*b*x^3