3.2447 \(\int x^{7/3} (a^{10/3}-x^{10/3})^{19/7} \, dx\)

Optimal. Leaf size=21 \[ -\frac{21}{260} \left (a^{10/3}-x^{10/3}\right )^{26/7} \]

[Out]

(-21*(a^(10/3) - x^(10/3))^(26/7))/260

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Rubi [A]  time = 0.0044601, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 23, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.043, Rules used = {261} \[ -\frac{21}{260} \left (a^{10/3}-x^{10/3}\right )^{26/7} \]

Antiderivative was successfully verified.

[In]

Int[x^(7/3)*(a^(10/3) - x^(10/3))^(19/7),x]

[Out]

(-21*(a^(10/3) - x^(10/3))^(26/7))/260

Rule 261

Int[(x_)^(m_.)*((a_) + (b_.)*(x_)^(n_))^(p_), x_Symbol] :> Simp[(a + b*x^n)^(p + 1)/(b*n*(p + 1)), x] /; FreeQ
[{a, b, m, n, p}, x] && EqQ[m, n - 1] && NeQ[p, -1]

Rubi steps

\begin{align*} \int x^{7/3} \left (a^{10/3}-x^{10/3}\right )^{19/7} \, dx &=-\frac{21}{260} \left (a^{10/3}-x^{10/3}\right )^{26/7}\\ \end{align*}

Mathematica [A]  time = 0.010714, size = 21, normalized size = 1. \[ -\frac{21}{260} \left (a^{10/3}-x^{10/3}\right )^{26/7} \]

Antiderivative was successfully verified.

[In]

Integrate[x^(7/3)*(a^(10/3) - x^(10/3))^(19/7),x]

[Out]

(-21*(a^(10/3) - x^(10/3))^(26/7))/260

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Maple [A]  time = 0.003, size = 14, normalized size = 0.7 \begin{align*} -{\frac{21}{260} \left ({a}^{{\frac{10}{3}}}-{x}^{{\frac{10}{3}}} \right ) ^{{\frac{26}{7}}}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^(7/3)*(a^(10/3)-x^(10/3))^(19/7),x)

[Out]

-21/260*(a^(10/3)-x^(10/3))^(26/7)

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Maxima [A]  time = 0.993103, size = 18, normalized size = 0.86 \begin{align*} -\frac{21}{260} \,{\left (a^{\frac{10}{3}} - x^{\frac{10}{3}}\right )}^{\frac{26}{7}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^(7/3)*(a^(10/3)-x^(10/3))^(19/7),x, algorithm="maxima")

[Out]

-21/260*(a^(10/3) - x^(10/3))^(26/7)

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Fricas [F(-1)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^(7/3)*(a^(10/3)-x^(10/3))^(19/7),x, algorithm="fricas")

[Out]

Timed out

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Sympy [F(-1)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x**(7/3)*(a**(10/3)-x**(10/3))**(19/7),x)

[Out]

Timed out

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Giac [B]  time = 1.27111, size = 109, normalized size = 5.19 \begin{align*} -\frac{7}{20} \,{\left (a^{\frac{10}{3}} - x^{\frac{10}{3}}\right )}^{\frac{12}{7}} a^{\frac{20}{3}} + \frac{21}{95} \,{\left (a^{\frac{10}{3}} - x^{\frac{10}{3}}\right )}^{\frac{19}{7}} a^{\frac{10}{3}} + \frac{7}{380} \,{\left (19 \,{\left (a^{\frac{10}{3}} - x^{\frac{10}{3}}\right )}^{\frac{12}{7}} a^{\frac{10}{3}} - 12 \,{\left (a^{\frac{10}{3}} - x^{\frac{10}{3}}\right )}^{\frac{19}{7}}\right )} a^{\frac{10}{3}} - \frac{21}{260} \,{\left (a^{\frac{10}{3}} - x^{\frac{10}{3}}\right )}^{\frac{26}{7}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^(7/3)*(a^(10/3)-x^(10/3))^(19/7),x, algorithm="giac")

[Out]

-7/20*(a^(10/3) - x^(10/3))^(12/7)*a^(20/3) + 21/95*(a^(10/3) - x^(10/3))^(19/7)*a^(10/3) + 7/380*(19*(a^(10/3
) - x^(10/3))^(12/7)*a^(10/3) - 12*(a^(10/3) - x^(10/3))^(19/7))*a^(10/3) - 21/260*(a^(10/3) - x^(10/3))^(26/7
)