3.780 \(\int \frac{\sqrt [6]{x}+\sqrt [5]{x^3}}{\sqrt{x}} \, dx\)

Optimal. Leaf size=26 \[ \frac{3 x^{2/3}}{2}+\frac{10}{11} \sqrt [5]{x^3} \sqrt{x} \]

[Out]

(3*x^(2/3))/2 + (10*Sqrt[x]*(x^3)^(1/5))/11

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Rubi [A]  time = 0.0149048, antiderivative size = 26, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.158 \[ \frac{3 x^{2/3}}{2}+\frac{10}{11} \sqrt [5]{x^3} \sqrt{x} \]

Antiderivative was successfully verified.

[In]  Int[(x^(1/6) + (x^3)^(1/5))/Sqrt[x],x]

[Out]

(3*x^(2/3))/2 + (10*Sqrt[x]*(x^3)^(1/5))/11

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Rubi in Sympy [A]  time = 2.43389, size = 22, normalized size = 0.85 \[ \frac{3 x^{\frac{2}{3}}}{2} + \frac{10 \sqrt{x} \sqrt [5]{x^{3}}}{11} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((x**(1/6)+(x**3)**(1/5))/x**(1/2),x)

[Out]

3*x**(2/3)/2 + 10*sqrt(x)*(x**3)**(1/5)/11

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Mathematica [A]  time = 0.0157092, size = 26, normalized size = 1. \[ \frac{3 x^{2/3}}{2}+\frac{10}{11} \sqrt [5]{x^3} \sqrt{x} \]

Antiderivative was successfully verified.

[In]  Integrate[(x^(1/6) + (x^3)^(1/5))/Sqrt[x],x]

[Out]

(3*x^(2/3))/2 + (10*Sqrt[x]*(x^3)^(1/5))/11

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Maple [A]  time = 0.005, size = 17, normalized size = 0.7 \[{\frac{3}{2}{x}^{{\frac{2}{3}}}}+{\frac{10}{11}\sqrt [5]{{x}^{3}}\sqrt{x}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((x^(1/6)+(x^3)^(1/5))/x^(1/2),x)

[Out]

3/2*x^(2/3)+10/11*(x^3)^(1/5)*x^(1/2)

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Maxima [A]  time = 0.709692, size = 22, normalized size = 0.85 \[ \frac{10}{11} \,{\left (x^{3}\right )}^{\frac{1}{5}} \sqrt{x} + \frac{3}{2} \, x^{\frac{2}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(((x^3)^(1/5) + x^(1/6))/sqrt(x),x, algorithm="maxima")

[Out]

10/11*(x^3)^(1/5)*sqrt(x) + 3/2*x^(2/3)

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Fricas [A]  time = 0.266713, size = 26, normalized size = 1. \[ \frac{20 \,{\left (x^{3}\right )}^{\frac{1}{5}} x^{\frac{5}{6}} + 33 \, x}{22 \, x^{\frac{1}{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(((x^3)^(1/5) + x^(1/6))/sqrt(x),x, algorithm="fricas")

[Out]

1/22*(20*(x^3)^(1/5)*x^(5/6) + 33*x)/x^(1/3)

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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((x**(1/6)+(x**3)**(1/5))/x**(1/2),x)

[Out]

Timed out

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GIAC/XCAS [A]  time = 0.261164, size = 15, normalized size = 0.58 \[ \frac{10}{11} \, x^{\frac{11}{10}} + \frac{3}{2} \, x^{\frac{2}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(((x^3)^(1/5) + x^(1/6))/sqrt(x),x, algorithm="giac")

[Out]

10/11*x^(11/10) + 3/2*x^(2/3)