3.211 \(\int \frac{a+b x^3}{x^2} \, dx\)

Optimal. Leaf size=15 \[ \frac{b x^2}{2}-\frac{a}{x} \]

[Out]

-(a/x) + (b*x^2)/2

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Rubi [A]  time = 0.0130924, 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 \[ \frac{b x^2}{2}-\frac{a}{x} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x^3)/x^2,x]

[Out]

-(a/x) + (b*x^2)/2

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

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x**3+a)/x**2,x)

[Out]

-a/x + b*Integral(x, x)

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Mathematica [A]  time = 0.00187862, size = 15, normalized size = 1. \[ \frac{b x^2}{2}-\frac{a}{x} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*x^3)/x^2,x]

[Out]

-(a/x) + (b*x^2)/2

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Maple [A]  time = 0.005, size = 14, normalized size = 0.9 \[ -{\frac{a}{x}}+{\frac{b{x}^{2}}{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^3+a)/x^2,x)

[Out]

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

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Maxima [A]  time = 1.44221, size = 18, normalized size = 1.2 \[ \frac{1}{2} \, b x^{2} - \frac{a}{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)/x^2,x, algorithm="maxima")

[Out]

1/2*b*x^2 - a/x

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Fricas [A]  time = 0.211457, size = 19, normalized size = 1.27 \[ \frac{b x^{3} - 2 \, a}{2 \, x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)/x^2,x, algorithm="fricas")

[Out]

1/2*(b*x^3 - 2*a)/x

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Sympy [A]  time = 1.02542, size = 8, normalized size = 0.53 \[ - \frac{a}{x} + \frac{b x^{2}}{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**3+a)/x**2,x)

[Out]

-a/x + b*x**2/2

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GIAC/XCAS [A]  time = 0.233351, size = 18, normalized size = 1.2 \[ \frac{1}{2} \, b x^{2} - \frac{a}{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)/x^2,x, algorithm="giac")

[Out]

1/2*b*x^2 - a/x