3.2443 \(\int \left (a+\frac{b}{x^{3/5}}\right )^{2/3} \, dx\)

Optimal. Leaf size=18 \[ \frac{x \left (a+\frac{b}{x^{3/5}}\right )^{5/3}}{a} \]

[Out]

((a + b/x^(3/5))^(5/3)*x)/a

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Rubi [A]  time = 0.013214, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{x \left (a+\frac{b}{x^{3/5}}\right )^{5/3}}{a} \]

Antiderivative was successfully verified.

[In]  Int[(a + b/x^(3/5))^(2/3),x]

[Out]

((a + b/x^(3/5))^(5/3)*x)/a

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Rubi in Sympy [A]  time = 1.34892, size = 14, normalized size = 0.78 \[ \frac{x \left (a + \frac{b}{x^{\frac{3}{5}}}\right )^{\frac{5}{3}}}{a} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((a+b/x**(3/5))**(2/3),x)

[Out]

x*(a + b/x**(3/5))**(5/3)/a

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Mathematica [A]  time = 0.0345687, size = 28, normalized size = 1.56 \[ \frac{\left (a+\frac{b}{x^{3/5}}\right )^{2/3} \left (a x+b x^{2/5}\right )}{a} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b/x^(3/5))^(2/3),x]

[Out]

((a + b/x^(3/5))^(2/3)*(b*x^(2/5) + a*x))/a

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Maple [F]  time = 0.023, size = 0, normalized size = 0. \[ \int \left ( a+{b{x}^{-{\frac{3}{5}}}} \right ) ^{{\frac{2}{3}}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((a+b/x^(3/5))^(2/3),x)

[Out]

int((a+b/x^(3/5))^(2/3),x)

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Maxima [A]  time = 1.44677, size = 19, normalized size = 1.06 \[ \frac{{\left (a + \frac{b}{x^{\frac{3}{5}}}\right )}^{\frac{5}{3}} x}{a} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a + b/x^(3/5))^(2/3),x, algorithm="maxima")

[Out]

(a + b/x^(3/5))^(5/3)*x/a

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

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a + b/x^(3/5))^(2/3),x, algorithm="fricas")

[Out]

Timed out

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

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a+b/x**(3/5))**(2/3),x)

[Out]

Timed out

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GIAC/XCAS [F]  time = 0., size = 0, normalized size = 0. \[ \int{\left (a + \frac{b}{x^{\frac{3}{5}}}\right )}^{\frac{2}{3}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a + b/x^(3/5))^(2/3),x, algorithm="giac")

[Out]

integrate((a + b/x^(3/5))^(2/3), x)