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

Optimal. Leaf size=12 \[ b x-\frac{a}{2 x^2} \]

[Out]

-a/(2*x^2) + b*x

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Rubi [A]  time = 0.0119194, antiderivative size = 12, 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 \[ b x-\frac{a}{2 x^2} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x^3)/x^3,x]

[Out]

-a/(2*x^2) + b*x

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

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-a/(2*x**2) + Integral(b, x)

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Mathematica [A]  time = 0.00161559, size = 12, normalized size = 1. \[ b x-\frac{a}{2 x^2} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*x^3)/x^3,x]

[Out]

-a/(2*x^2) + b*x

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Maple [A]  time = 0.003, size = 11, normalized size = 0.9 \[ -{\frac{a}{2\,{x}^{2}}}+bx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^3+a)/x^3,x)

[Out]

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

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Maxima [A]  time = 1.4471, size = 14, normalized size = 1.17 \[ b x - \frac{a}{2 \, x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

b*x - 1/2*a/x^2

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Fricas [A]  time = 0.208041, size = 20, normalized size = 1.67 \[ \frac{2 \, b x^{3} - a}{2 \, x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/2*(2*b*x^3 - a)/x^2

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Sympy [A]  time = 1.00311, size = 8, normalized size = 0.67 \[ - \frac{a}{2 x^{2}} + b x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**3+a)/x**3,x)

[Out]

-a/(2*x**2) + b*x

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GIAC/XCAS [A]  time = 0.217769, size = 14, normalized size = 1.17 \[ b x - \frac{a}{2 \, x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

b*x - 1/2*a/x^2