3.7.41 \(\int \frac {1-\sqrt {x}}{\sqrt [3]{x}} \, dx\)

Optimal. Leaf size=19 \[ \frac {3 x^{2/3}}{2}-\frac {6 x^{7/6}}{7} \]

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Rubi [A]  time = 0.00, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {14} \begin {gather*} \frac {3 x^{2/3}}{2}-\frac {6 x^{7/6}}{7} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(1 - Sqrt[x])/x^(1/3),x]

[Out]

(3*x^(2/3))/2 - (6*x^(7/6))/7

Rule 14

Int[(u_)*((c_.)*(x_))^(m_.), x_Symbol] :> Int[ExpandIntegrand[(c*x)^m*u, x], x] /; FreeQ[{c, m}, x] && SumQ[u]
&&  !LinearQ[u, x] &&  !MatchQ[u, (a_) + (b_.)*(v_) /; FreeQ[{a, b}, x] && InverseFunctionQ[v]]

Rubi steps

\begin {align*} \int \frac {1-\sqrt {x}}{\sqrt [3]{x}} \, dx &=\int \left (\frac {1}{\sqrt [3]{x}}-\sqrt [6]{x}\right ) \, dx\\ &=\frac {3 x^{2/3}}{2}-\frac {6 x^{7/6}}{7}\\ \end {align*}

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Mathematica [A]  time = 0.00, size = 19, normalized size = 1.00 \begin {gather*} \frac {3 x^{2/3}}{2}-\frac {6 x^{7/6}}{7} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(1 - Sqrt[x])/x^(1/3),x]

[Out]

(3*x^(2/3))/2 - (6*x^(7/6))/7

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IntegrateAlgebraic [A]  time = 0.02, size = 19, normalized size = 1.00 \begin {gather*} -\frac {3}{14} \left (4 x^{7/6}-7 x^{2/3}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

IntegrateAlgebraic[(1 - Sqrt[x])/x^(1/3),x]

[Out]

(-3*(-7*x^(2/3) + 4*x^(7/6)))/14

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fricas [A]  time = 0.51, size = 11, normalized size = 0.58 \begin {gather*} -\frac {6}{7} \, x^{\frac {7}{6}} + \frac {3}{2} \, x^{\frac {2}{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-x^(1/2))/x^(1/3),x, algorithm="fricas")

[Out]

-6/7*x^(7/6) + 3/2*x^(2/3)

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giac [A]  time = 0.37, size = 11, normalized size = 0.58 \begin {gather*} -\frac {6}{7} \, x^{\frac {7}{6}} + \frac {3}{2} \, x^{\frac {2}{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-x^(1/2))/x^(1/3),x, algorithm="giac")

[Out]

-6/7*x^(7/6) + 3/2*x^(2/3)

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maple [A]  time = 0.00, size = 12, normalized size = 0.63 \begin {gather*} -\frac {6 x^{\frac {7}{6}}}{7}+\frac {3 x^{\frac {2}{3}}}{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((1-x^(1/2))/x^(1/3),x)

[Out]

3/2*x^(2/3)-6/7*x^(7/6)

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maxima [A]  time = 0.48, size = 11, normalized size = 0.58 \begin {gather*} -\frac {6}{7} \, x^{\frac {7}{6}} + \frac {3}{2} \, x^{\frac {2}{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-x^(1/2))/x^(1/3),x, algorithm="maxima")

[Out]

-6/7*x^(7/6) + 3/2*x^(2/3)

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mupad [B]  time = 0.02, size = 12, normalized size = 0.63 \begin {gather*} -\frac {3\,x^{2/3}\,\left (4\,\sqrt {x}-7\right )}{14} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(x^(1/2) - 1)/x^(1/3),x)

[Out]

-(3*x^(2/3)*(4*x^(1/2) - 7))/14

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sympy [A]  time = 1.53, size = 15, normalized size = 0.79 \begin {gather*} - \frac {6 x^{\frac {7}{6}}}{7} + \frac {3 x^{\frac {2}{3}}}{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-x**(1/2))/x**(1/3),x)

[Out]

-6*x**(7/6)/7 + 3*x**(2/3)/2

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