3.2289 \(\int (a+b \sqrt [3]{x}) \, dx\)

Optimal. Leaf size=14 \[ a x+\frac{3}{4} b x^{4/3} \]

[Out]

a*x + (3*b*x^(4/3))/4

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Rubi [A]  time = 0.002333, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ a x+\frac{3}{4} b x^{4/3} \]

Antiderivative was successfully verified.

[In]

Int[a + b*x^(1/3),x]

[Out]

a*x + (3*b*x^(4/3))/4

Rubi steps

\begin{align*} \int \left (a+b \sqrt [3]{x}\right ) \, dx &=a x+\frac{3}{4} b x^{4/3}\\ \end{align*}

Mathematica [A]  time = 0.0014258, size = 14, normalized size = 1. \[ a x+\frac{3}{4} b x^{4/3} \]

Antiderivative was successfully verified.

[In]

Integrate[a + b*x^(1/3),x]

[Out]

a*x + (3*b*x^(4/3))/4

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Maple [A]  time = 0., size = 11, normalized size = 0.8 \begin{align*} ax+{\frac{3\,b}{4}{x}^{{\frac{4}{3}}}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

a*x+3/4*b*x^(4/3)

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Maxima [A]  time = 0.983134, size = 14, normalized size = 1. \begin{align*} \frac{3}{4} \, b x^{\frac{4}{3}} + a x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

3/4*b*x^(4/3) + a*x

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Fricas [A]  time = 1.47942, size = 28, normalized size = 2. \begin{align*} \frac{3}{4} \, b x^{\frac{4}{3}} + a x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

3/4*b*x^(4/3) + a*x

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Sympy [A]  time = 0.055042, size = 12, normalized size = 0.86 \begin{align*} a x + \frac{3 b x^{\frac{4}{3}}}{4} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

a*x + 3*b*x**(4/3)/4

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Giac [A]  time = 1.08837, size = 14, normalized size = 1. \begin{align*} \frac{3}{4} \, b x^{\frac{4}{3}} + a x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

3/4*b*x^(4/3) + a*x