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

Optimal. Leaf size=19 \[ \frac{1}{3} b^2 x^2 \sqrt{b x^2} \]

[Out]

(b^2*x^2*Sqrt[b*x^2])/3

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Rubi [A]  time = 0.00790422, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{1}{3} b^2 x^2 \sqrt{b x^2} \]

Antiderivative was successfully verified.

[In]  Int[(b*x^2)^(5/2)/x^3,x]

[Out]

(b^2*x^2*Sqrt[b*x^2])/3

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Rubi in Sympy [A]  time = 2.4331, size = 10, normalized size = 0.53 \[ \frac{b \left (b x^{2}\right )^{\frac{3}{2}}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

b*(b*x**2)**(3/2)/3

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Mathematica [A]  time = 0.00347502, size = 16, normalized size = 0.84 \[ \frac{\left (b x^2\right )^{5/2}}{3 x^2} \]

Antiderivative was successfully verified.

[In]  Integrate[(b*x^2)^(5/2)/x^3,x]

[Out]

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

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Maple [A]  time = 0.003, size = 13, normalized size = 0.7 \[{\frac{1}{3\,{x}^{2}} \left ( b{x}^{2} \right ) ^{{\frac{5}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^2)^(5/2)/x^3,x)

[Out]

1/3*(b*x^2)^(5/2)/x^2

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Maxima [F]  time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: RuntimeError} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

Exception raised: RuntimeError

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Fricas [A]  time = 0.249422, size = 20, normalized size = 1.05 \[ \frac{1}{3} \, \sqrt{b x^{2}} b^{2} x^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/3*sqrt(b*x^2)*b^2*x^2

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Sympy [A]  time = 4.6241, size = 15, normalized size = 0.79 \[ \frac{b^{\frac{5}{2}} \left (x^{2}\right )^{\frac{5}{2}}}{3 x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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GIAC/XCAS [A]  time = 0.225925, size = 14, normalized size = 0.74 \[ \frac{1}{3} \, b^{\frac{5}{2}} x^{3}{\rm sign}\left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/3*b^(5/2)*x^3*sign(x)