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

Optimal. Leaf size=13 \[ a \log (x)+\frac{b x^3}{3} \]

[Out]

(b*x^3)/3 + a*Log[x]

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Rubi [A]  time = 0.0109953, antiderivative size = 13, 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 \[ a \log (x)+\frac{b x^3}{3} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x^3)/x,x]

[Out]

(b*x^3)/3 + a*Log[x]

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Rubi in Sympy [A]  time = 2.75585, size = 10, normalized size = 0.77 \[ a \log{\left (x \right )} + \frac{b x^{3}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x**3+a)/x,x)

[Out]

a*log(x) + b*x**3/3

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Mathematica [A]  time = 0.00304368, size = 13, normalized size = 1. \[ a \log (x)+\frac{b x^3}{3} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*x^3)/x,x]

[Out]

(b*x^3)/3 + a*Log[x]

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Maple [A]  time = 0.003, size = 12, normalized size = 0.9 \[{\frac{b{x}^{3}}{3}}+a\ln \left ( x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^3+a)/x,x)

[Out]

1/3*b*x^3+a*ln(x)

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Maxima [A]  time = 1.42253, size = 19, normalized size = 1.46 \[ \frac{1}{3} \, b x^{3} + \frac{1}{3} \, a \log \left (x^{3}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/3*b*x^3 + 1/3*a*log(x^3)

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Fricas [A]  time = 0.211994, size = 15, normalized size = 1.15 \[ \frac{1}{3} \, b x^{3} + a \log \left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/3*b*x^3 + a*log(x)

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Sympy [A]  time = 0.154558, size = 10, normalized size = 0.77 \[ a \log{\left (x \right )} + \frac{b x^{3}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**3+a)/x,x)

[Out]

a*log(x) + b*x**3/3

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GIAC/XCAS [A]  time = 0.26586, size = 16, normalized size = 1.23 \[ \frac{1}{3} \, b x^{3} + a{\rm ln}\left ({\left | x \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/3*b*x^3 + a*ln(abs(x))