3.2398 \(\int (a+\frac {b}{\sqrt [3]{x}}) \, dx\)

Optimal. Leaf size=14 \[ a x+\frac {3}{2} b x^{2/3} \]

[Out]

3/2*b*x^(2/3)+a*x

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Rubi [A]  time = 0.00, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ a x+\frac {3}{2} b x^{2/3} \]

Antiderivative was successfully verified.

[In]

Int[a + b/x^(1/3),x]

[Out]

(3*b*x^(2/3))/2 + a*x

Rubi steps

\begin {align*} \int \left (a+\frac {b}{\sqrt [3]{x}}\right ) \, dx &=\frac {3}{2} b x^{2/3}+a x\\ \end {align*}

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Mathematica [A]  time = 0.00, size = 14, normalized size = 1.00 \[ a x+\frac {3}{2} b x^{2/3} \]

Antiderivative was successfully verified.

[In]

Integrate[a + b/x^(1/3),x]

[Out]

(3*b*x^(2/3))/2 + a*x

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fricas [A]  time = 0.87, size = 10, normalized size = 0.71 \[ a x + \frac {3}{2} \, b x^{\frac {2}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

a*x + 3/2*b*x^(2/3)

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giac [A]  time = 0.15, size = 10, normalized size = 0.71 \[ a x + \frac {3}{2} \, b x^{\frac {2}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

a*x + 3/2*b*x^(2/3)

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maple [A]  time = 0.00, size = 11, normalized size = 0.79 \[ a x +\frac {3 b \,x^{\frac {2}{3}}}{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(a+b/x^(1/3),x)

[Out]

3/2*b*x^(2/3)+a*x

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maxima [A]  time = 0.66, size = 10, normalized size = 0.71 \[ a x + \frac {3}{2} \, b x^{\frac {2}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

a*x + 3/2*b*x^(2/3)

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mupad [B]  time = 0.03, size = 10, normalized size = 0.71 \[ a\,x+\frac {3\,b\,x^{2/3}}{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(a + b/x^(1/3),x)

[Out]

a*x + (3*b*x^(2/3))/2

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sympy [A]  time = 0.08, size = 12, normalized size = 0.86 \[ a x + \frac {3 b x^{\frac {2}{3}}}{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(a+b/x**(1/3),x)

[Out]

a*x + 3*b*x**(2/3)/2

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