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

Optimal. Leaf size=17 \[ \frac{2}{11} b x^4 \sqrt{b x^3} \]

[Out]

(2*b*x^4*Sqrt[b*x^3])/11

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Rubi [A]  time = 0.00774167, antiderivative size = 17, 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 \[ \frac{2}{11} b x^4 \sqrt{b x^3} \]

Antiderivative was successfully verified.

[In]  Int[(b*x^3)^(3/2),x]

[Out]

(2*b*x^4*Sqrt[b*x^3])/11

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Rubi in Sympy [A]  time = 1.30868, size = 15, normalized size = 0.88 \[ \frac{2 b x^{4} \sqrt{b x^{3}}}{11} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

2*b*x**4*sqrt(b*x**3)/11

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Mathematica [A]  time = 0.00273681, size = 14, normalized size = 0.82 \[ \frac{2}{11} x \left (b x^3\right )^{3/2} \]

Antiderivative was successfully verified.

[In]  Integrate[(b*x^3)^(3/2),x]

[Out]

(2*x*(b*x^3)^(3/2))/11

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Maple [A]  time = 0.003, size = 11, normalized size = 0.7 \[{\frac{2\,x}{11} \left ( b{x}^{3} \right ) ^{{\frac{3}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^3)^(3/2),x)

[Out]

2/11*x*(b*x^3)^(3/2)

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Maxima [A]  time = 1.4247, size = 14, normalized size = 0.82 \[ \frac{2}{11} \, \left (b x^{3}\right )^{\frac{3}{2}} x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

2/11*(b*x^3)^(3/2)*x

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Fricas [A]  time = 0.225569, size = 18, normalized size = 1.06 \[ \frac{2}{11} \, \sqrt{b x^{3}} b x^{4} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

2/11*sqrt(b*x^3)*b*x^4

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Sympy [A]  time = 1.12844, size = 15, normalized size = 0.88 \[ \frac{2 b^{\frac{3}{2}} x \left (x^{3}\right )^{\frac{3}{2}}}{11} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**3)**(3/2),x)

[Out]

2*b**(3/2)*x*(x**3)**(3/2)/11

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GIAC/XCAS [A]  time = 0.216178, size = 18, normalized size = 1.06 \[ \frac{2}{11} \, \sqrt{b x} b x^{5}{\rm sign}\left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

2/11*sqrt(b*x)*b*x^5*sign(x)