3.2283 \(\int \frac{a+b \sqrt [3]{x}}{x} \, dx\)

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

[Out]

3*b*x^(1/3) + a*Log[x]

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Rubi [A]  time = 0.015596, 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 \[ a \log (x)+3 b \sqrt [3]{x} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x^(1/3))/x,x]

[Out]

3*b*x^(1/3) + a*Log[x]

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Rubi in Sympy [A]  time = 2.81745, size = 12, normalized size = 0.92 \[ a \log{\left (x \right )} + 3 b \sqrt [3]{x} \]

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)

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Mathematica [A]  time = 0.00759096, size = 13, normalized size = 1. \[ a \log (x)+3 b \sqrt [3]{x} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*x^(1/3))/x,x]

[Out]

3*b*x^(1/3) + a*Log[x]

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Maple [A]  time = 0.004, size = 12, normalized size = 0.9 \[ 3\,b\sqrt [3]{x}+a\ln \left ( x \right ) \]

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)

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Maxima [A]  time = 1.43977, size = 15, normalized size = 1.15 \[ a \log \left (x\right ) + 3 \, b x^{\frac{1}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

a*log(x) + 3*b*x^(1/3)

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Fricas [A]  time = 0.218097, size = 19, normalized size = 1.46 \[ 3 \, a \log \left (x^{\frac{1}{3}}\right ) + 3 \, b x^{\frac{1}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

3*a*log(x^(1/3)) + 3*b*x^(1/3)

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Sympy [A]  time = 0.710171, size = 12, normalized size = 0.92 \[ a \log{\left (x \right )} + 3 b \sqrt [3]{x} \]

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)

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GIAC/XCAS [A]  time = 0.269308, size = 16, normalized size = 1.23 \[ a{\rm ln}\left ({\left | x \right |}\right ) + 3 \, b x^{\frac{1}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

a*ln(abs(x)) + 3*b*x^(1/3)