3.104 \(\int \sqrt [3]{b x} \, dx\)

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

[Out]

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

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Rubi [A]  time = 0.0012486, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143, Rules used = {32} \[ \frac{3 (b x)^{4/3}}{4 b} \]

Antiderivative was successfully verified.

[In]

Int[(b*x)^(1/3),x]

[Out]

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

Rule 32

Int[((a_.) + (b_.)*(x_))^(m_), x_Symbol] :> Simp[(a + b*x)^(m + 1)/(b*(m + 1)), x] /; FreeQ[{a, b, m}, x] && N
eQ[m, -1]

Rubi steps

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

Mathematica [A]  time = 0.0008529, size = 12, normalized size = 0.86 \[ \frac{3}{4} x \sqrt [3]{b x} \]

Antiderivative was successfully verified.

[In]

Integrate[(b*x)^(1/3),x]

[Out]

(3*x*(b*x)^(1/3))/4

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Maple [A]  time = 0.001, size = 9, normalized size = 0.6 \begin{align*}{\frac{3\,x}{4}\sqrt [3]{bx}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

3/4*x*(b*x)^(1/3)

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Maxima [A]  time = 0.957675, size = 14, normalized size = 1. \begin{align*} \frac{3 \, \left (b x\right )^{\frac{4}{3}}}{4 \, b} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Fricas [A]  time = 1.63946, size = 26, normalized size = 1.86 \begin{align*} \frac{3}{4} \, \left (b x\right )^{\frac{1}{3}} x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

3/4*(b*x)^(1/3)*x

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Sympy [A]  time = 0.088943, size = 10, normalized size = 0.71 \begin{align*} \frac{3 \left (b x\right )^{\frac{4}{3}}}{4 b} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

3*(b*x)**(4/3)/(4*b)

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Giac [A]  time = 1.13355, size = 11, normalized size = 0.79 \begin{align*} \frac{3}{4} \, \left (b x\right )^{\frac{1}{3}} x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

3/4*(b*x)^(1/3)*x