3.2392 \(\int \frac{a+\frac{b}{\sqrt [3]{x}}}{x} \, dx\)

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

[Out]

(-3*b)/x^(1/3) + a*Log[x]

_______________________________________________________________________________________

Rubi [A]  time = 0.0148795, antiderivative size = 13, 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 \[ a \log (x)-\frac{3 b}{\sqrt [3]{x}} \]

Antiderivative was successfully verified.

[In]  Int[(a + b/x^(1/3))/x,x]

[Out]

(-3*b)/x^(1/3) + a*Log[x]

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 2.86631, size = 12, normalized size = 0.92 \[ a \log{\left (x \right )} - \frac{3 b}{\sqrt [3]{x}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((a+b/x**(1/3))/x,x)

[Out]

a*log(x) - 3*b/x**(1/3)

_______________________________________________________________________________________

Mathematica [A]  time = 0.0113008, size = 13, normalized size = 1. \[ a \log (x)-\frac{3 b}{\sqrt [3]{x}} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b/x^(1/3))/x,x]

[Out]

(-3*b)/x^(1/3) + a*Log[x]

_______________________________________________________________________________________

Maple [A]  time = 0.009, size = 12, normalized size = 0.9 \[ -3\,{\frac{b}{\sqrt [3]{x}}}+a\ln \left ( x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((a+b/x^(1/3))/x,x)

[Out]

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

_______________________________________________________________________________________

Maxima [A]  time = 1.42461, size = 15, normalized size = 1.15 \[ a \log \left (x\right ) - \frac{3 \, b}{x^{\frac{1}{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a + b/x^(1/3))/x,x, algorithm="maxima")

[Out]

a*log(x) - 3*b/x^(1/3)

_______________________________________________________________________________________

Fricas [A]  time = 0.224472, size = 24, normalized size = 1.85 \[ \frac{3 \,{\left (a x^{\frac{1}{3}} \log \left (x^{\frac{1}{3}}\right ) - b\right )}}{x^{\frac{1}{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a + b/x^(1/3))/x,x, algorithm="fricas")

[Out]

3*(a*x^(1/3)*log(x^(1/3)) - b)/x^(1/3)

_______________________________________________________________________________________

Sympy [A]  time = 1.56687, size = 12, normalized size = 0.92 \[ a \log{\left (x \right )} - \frac{3 b}{\sqrt [3]{x}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a+b/x**(1/3))/x,x)

[Out]

a*log(x) - 3*b/x**(1/3)

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.219377, size = 16, normalized size = 1.23 \[ a{\rm ln}\left ({\left | x \right |}\right ) - \frac{3 \, b}{x^{\frac{1}{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a + b/x^(1/3))/x,x, algorithm="giac")

[Out]

a*ln(abs(x)) - 3*b/x^(1/3)