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

Optimal. Leaf size=15 \[ \frac{b x^3}{3}-\frac{a}{x} \]

[Out]

-(a/x) + (b*x^3)/3

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Rubi [A]  time = 0.0131727, antiderivative size = 15, 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 \[ \frac{b x^3}{3}-\frac{a}{x} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x^4)/x^2,x]

[Out]

-(a/x) + (b*x^3)/3

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Rubi in Sympy [A]  time = 2.8234, size = 8, normalized size = 0.53 \[ - \frac{a}{x} + \frac{b x^{3}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-a/x + b*x**3/3

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Mathematica [A]  time = 0.00351181, size = 15, normalized size = 1. \[ \frac{b x^3}{3}-\frac{a}{x} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*x^4)/x^2,x]

[Out]

-(a/x) + (b*x^3)/3

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Maple [A]  time = 0.004, size = 14, normalized size = 0.9 \[ -{\frac{a}{x}}+{\frac{b{x}^{3}}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^4+a)/x^2,x)

[Out]

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

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Maxima [A]  time = 1.43182, size = 18, normalized size = 1.2 \[ \frac{1}{3} \, b x^{3} - \frac{a}{x} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/3*b*x^3 - a/x

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Fricas [A]  time = 0.215554, size = 19, normalized size = 1.27 \[ \frac{b x^{4} - 3 \, a}{3 \, x} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/3*(b*x^4 - 3*a)/x

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Sympy [A]  time = 0.96271, size = 8, normalized size = 0.53 \[ - \frac{a}{x} + \frac{b x^{3}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**4+a)/x**2,x)

[Out]

-a/x + b*x**3/3

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GIAC/XCAS [A]  time = 0.217517, size = 18, normalized size = 1.2 \[ \frac{1}{3} \, b x^{3} - \frac{a}{x} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/3*b*x^3 - a/x