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

Optimal. Leaf size=12 \[ a x+\frac{b x^3}{3} \]

[Out]

a*x + (b*x^3)/3

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Rubi [A]  time = 0.00977164, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ a x+\frac{b x^3}{3} \]

Antiderivative was successfully verified.

[In]  Int[(a*x + b*x^3)/x,x]

[Out]

a*x + (b*x^3)/3

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{b x^{3}}{3} + \int a\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

b*x**3/3 + Integral(a, x)

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Mathematica [A]  time = 0.000616287, size = 12, normalized size = 1. \[ a x+\frac{b x^3}{3} \]

Antiderivative was successfully verified.

[In]  Integrate[(a*x + b*x^3)/x,x]

[Out]

a*x + (b*x^3)/3

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Maple [A]  time = 0.002, size = 11, normalized size = 0.9 \[ ax+{\frac{b{x}^{3}}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^3+a*x)/x,x)

[Out]

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

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Maxima [A]  time = 1.36991, size = 14, normalized size = 1.17 \[ \frac{1}{3} \, b x^{3} + a x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/3*b*x^3 + a*x

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Fricas [A]  time = 0.197114, size = 14, normalized size = 1.17 \[ \frac{1}{3} \, b x^{3} + a x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/3*b*x^3 + a*x

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Sympy [A]  time = 0.03994, size = 8, normalized size = 0.67 \[ a x + \frac{b x^{3}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**3+a*x)/x,x)

[Out]

a*x + b*x**3/3

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GIAC/XCAS [A]  time = 0.21486, size = 14, normalized size = 1.17 \[ \frac{1}{3} \, b x^{3} + a x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/3*b*x^3 + a*x