3.115 \(\int \left (\frac{b}{x^4}\right )^{2/3} \, dx\)

Optimal. Leaf size=14 \[ -\frac{3}{5} x \left (\frac{b}{x^4}\right )^{2/3} \]

[Out]

(-3*(b/x^4)^(2/3)*x)/5

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Rubi [A]  time = 0.00728345, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222 \[ -\frac{3}{5} x \left (\frac{b}{x^4}\right )^{2/3} \]

Antiderivative was successfully verified.

[In]  Int[(b/x^4)^(2/3),x]

[Out]

(-3*(b/x^4)^(2/3)*x)/5

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Rubi in Sympy [A]  time = 1.25607, size = 14, normalized size = 1. \[ - \frac{3 x \left (\frac{b}{x^{4}}\right )^{\frac{2}{3}}}{5} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b/x**4)**(2/3),x)

[Out]

-3*x*(b/x**4)**(2/3)/5

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Mathematica [A]  time = 0.00203797, size = 14, normalized size = 1. \[ -\frac{3}{5} x \left (\frac{b}{x^4}\right )^{2/3} \]

Antiderivative was successfully verified.

[In]  Integrate[(b/x^4)^(2/3),x]

[Out]

(-3*(b/x^4)^(2/3)*x)/5

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Maple [A]  time = 0.003, size = 11, normalized size = 0.8 \[ -{\frac{3\,x}{5} \left ({\frac{b}{{x}^{4}}} \right ) ^{{\frac{2}{3}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b/x^4)^(2/3),x)

[Out]

-3/5*(b/x^4)^(2/3)*x

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Maxima [A]  time = 1.43787, size = 14, normalized size = 1. \[ -\frac{3}{5} \, x \left (\frac{b}{x^{4}}\right )^{\frac{2}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b/x^4)^(2/3),x, algorithm="maxima")

[Out]

-3/5*x*(b/x^4)^(2/3)

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Fricas [A]  time = 0.220657, size = 14, normalized size = 1. \[ -\frac{3}{5} \, x \left (\frac{b}{x^{4}}\right )^{\frac{2}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b/x^4)^(2/3),x, algorithm="fricas")

[Out]

-3/5*x*(b/x^4)^(2/3)

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Sympy [A]  time = 1.69174, size = 19, normalized size = 1.36 \[ - \frac{3 b^{\frac{2}{3}} x \left (\frac{1}{x^{4}}\right )^{\frac{2}{3}}}{5} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b/x**4)**(2/3),x)

[Out]

-3*b**(2/3)*x*(x**(-4))**(2/3)/5

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GIAC/XCAS [F]  time = 0., size = 0, normalized size = 0. \[ \int \left (\frac{b}{x^{4}}\right )^{\frac{2}{3}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b/x^4)^(2/3),x, algorithm="giac")

[Out]

integrate((b/x^4)^(2/3), x)