3.610 \(\int \frac{a+b x^4}{x^3} \, dx\)

Optimal. Leaf size=17 \[ \frac{b x^2}{2}-\frac{a}{2 x^2} \]

[Out]

-a/(2*x^2) + (b*x^2)/2

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Rubi [A]  time = 0.0140303, 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 \[ \frac{b x^2}{2}-\frac{a}{2 x^2} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x^4)/x^3,x]

[Out]

-a/(2*x^2) + (b*x^2)/2

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

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x**4+a)/x**3,x)

[Out]

-a/(2*x**2) + b*Integral(x, x)

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Mathematica [A]  time = 0.00205973, size = 17, normalized size = 1. \[ \frac{b x^2}{2}-\frac{a}{2 x^2} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*x^4)/x^3,x]

[Out]

-a/(2*x^2) + (b*x^2)/2

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Maple [A]  time = 0.005, size = 14, normalized size = 0.8 \[ -{\frac{a}{2\,{x}^{2}}}+{\frac{b{x}^{2}}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^4+a)/x^3,x)

[Out]

-1/2*a/x^2+1/2*b*x^2

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Maxima [A]  time = 1.43338, size = 18, normalized size = 1.06 \[ \frac{1}{2} \, b x^{2} - \frac{a}{2 \, x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^4 + a)/x^3,x, algorithm="maxima")

[Out]

1/2*b*x^2 - 1/2*a/x^2

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Fricas [A]  time = 0.22449, size = 19, normalized size = 1.12 \[ \frac{b x^{4} - a}{2 \, x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^4 + a)/x^3,x, algorithm="fricas")

[Out]

1/2*(b*x^4 - a)/x^2

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Sympy [A]  time = 0.977738, size = 12, normalized size = 0.71 \[ - \frac{a}{2 x^{2}} + \frac{b x^{2}}{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**4+a)/x**3,x)

[Out]

-a/(2*x**2) + b*x**2/2

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GIAC/XCAS [A]  time = 0.218288, size = 18, normalized size = 1.06 \[ \frac{1}{2} \, b x^{2} - \frac{a}{2 \, x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^4 + a)/x^3,x, algorithm="giac")

[Out]

1/2*b*x^2 - 1/2*a/x^2