3.142 \(\int \frac{b x^2+c x^4}{x^6} \, dx\)

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

[Out]

-b/(3*x^3) - c/x

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Rubi [A]  time = 0.0149077, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ -\frac{b}{3 x^3}-\frac{c}{x} \]

Antiderivative was successfully verified.

[In]  Int[(b*x^2 + c*x^4)/x^6,x]

[Out]

-b/(3*x^3) - c/x

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Rubi in Sympy [A]  time = 4.67684, size = 10, normalized size = 0.67 \[ - \frac{b}{3 x^{3}} - \frac{c}{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((c*x**4+b*x**2)/x**6,x)

[Out]

-b/(3*x**3) - c/x

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Mathematica [A]  time = 0.00358957, size = 15, normalized size = 1. \[ -\frac{b}{3 x^3}-\frac{c}{x} \]

Antiderivative was successfully verified.

[In]  Integrate[(b*x^2 + c*x^4)/x^6,x]

[Out]

-b/(3*x^3) - c/x

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Maple [A]  time = 0.007, size = 14, normalized size = 0.9 \[ -{\frac{b}{3\,{x}^{3}}}-{\frac{c}{x}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((c*x^4+b*x^2)/x^6,x)

[Out]

-1/3*b/x^3-c/x

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Maxima [A]  time = 0.682489, size = 18, normalized size = 1.2 \[ -\frac{3 \, c x^{2} + b}{3 \, x^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((c*x^4 + b*x^2)/x^6,x, algorithm="maxima")

[Out]

-1/3*(3*c*x^2 + b)/x^3

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Fricas [A]  time = 0.248548, size = 18, normalized size = 1.2 \[ -\frac{3 \, c x^{2} + b}{3 \, x^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((c*x^4 + b*x^2)/x^6,x, algorithm="fricas")

[Out]

-1/3*(3*c*x^2 + b)/x^3

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Sympy [A]  time = 1.08279, size = 14, normalized size = 0.93 \[ - \frac{b + 3 c x^{2}}{3 x^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((c*x**4+b*x**2)/x**6,x)

[Out]

-(b + 3*c*x**2)/(3*x**3)

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GIAC/XCAS [A]  time = 0.267519, size = 18, normalized size = 1.2 \[ -\frac{3 \, c x^{2} + b}{3 \, x^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((c*x^4 + b*x^2)/x^6,x, algorithm="giac")

[Out]

-1/3*(3*c*x^2 + b)/x^3