3.85 \(\int (b x)^{3/2} \, dx\)

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

[Out]

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

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Rubi [A]  time = 0.00678556, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143 \[ \frac{2 (b x)^{5/2}}{5 b} \]

Antiderivative was successfully verified.

[In]  Int[(b*x)^(3/2),x]

[Out]

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

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Rubi in Sympy [A]  time = 1.34173, size = 10, normalized size = 0.71 \[ \frac{2 \left (b x\right )^{\frac{5}{2}}}{5 b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x)**(3/2),x)

[Out]

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

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Mathematica [A]  time = 0.00177495, size = 12, normalized size = 0.86 \[ \frac{2}{5} x (b x)^{3/2} \]

Antiderivative was successfully verified.

[In]  Integrate[(b*x)^(3/2),x]

[Out]

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

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Maple [A]  time = 0.003, size = 9, normalized size = 0.6 \[{\frac{2\,x}{5} \left ( bx \right ) ^{{\frac{3}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x)^(3/2),x)

[Out]

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

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Maxima [A]  time = 1.43371, size = 14, normalized size = 1. \[ \frac{2 \, \left (b x\right )^{\frac{5}{2}}}{5 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Fricas [A]  time = 0.249105, size = 15, normalized size = 1.07 \[ \frac{2}{5} \, \sqrt{b x} b x^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Sympy [A]  time = 0.061012, size = 10, normalized size = 0.71 \[ \frac{2 \left (b x\right )^{\frac{5}{2}}}{5 b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x)**(3/2),x)

[Out]

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

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GIAC/XCAS [A]  time = 0.227453, size = 15, normalized size = 1.07 \[ \frac{2}{5} \, \sqrt{b x} b x^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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