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]

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

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Rubi [A]  time = 0.00, antiderivative size = 21, normalized size of antiderivative = 1.00, 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*}

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Mathematica [A]  time = 0.01, size = 21, normalized size = 1.00 \[ -\frac {21}{260} \left (a^{10/3}-x^{10/3}\right )^{26/7} \]

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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fricas [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]

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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giac [B]  time = 0.71, size = 81, normalized size = 3.86 \[ -\frac {7}{20} \, {\left (a^{\frac {10}{3}} - x^{\frac {10}{3}}\right )}^{\frac {12}{7}} a^{\frac {20}{3}} + \frac {21}{95} \, {\left (a^{\frac {10}{3}} - x^{\frac {10}{3}}\right )}^{\frac {19}{7}} a^{\frac {10}{3}} + \frac {7}{380} \, {\left (19 \, {\left (a^{\frac {10}{3}} - x^{\frac {10}{3}}\right )}^{\frac {12}{7}} a^{\frac {10}{3}} - 12 \, {\left (a^{\frac {10}{3}} - x^{\frac {10}{3}}\right )}^{\frac {19}{7}}\right )} a^{\frac {10}{3}} - \frac {21}{260} \, {\left (a^{\frac {10}{3}} - x^{\frac {10}{3}}\right )}^{\frac {26}{7}} \]

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
)

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maple [A]  time = 0.00, size = 14, normalized size = 0.67 \[ -\frac {21 \left (a^{\frac {10}{3}}-x^{\frac {10}{3}}\right )^{\frac {26}{7}}}{260} \]

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 = 0.47, size = 13, normalized size = 0.62 \[ -\frac {21}{260} \, {\left (a^{\frac {10}{3}} - x^{\frac {10}{3}}\right )}^{\frac {26}{7}} \]

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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mupad [B]  time = 2.04, size = 13, normalized size = 0.62 \[ -\frac {21\,{\left (a^{10/3}-x^{10/3}\right )}^{26/7}}{260} \]

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*(a^(10/3) - x^(10/3))^(26/7))/260

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sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]

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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