Optimal. Leaf size=20 \[ \frac{2 b x^n \sqrt{b x^n}}{3 n} \]
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Rubi [A] time = 0.0114605, antiderivative size = 20, 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 \[ \frac{2 b x^n \sqrt{b x^n}}{3 n} \]
Antiderivative was successfully verified.
[In] Int[(b*x^n)^(3/2)/x,x]
[Out]
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Rubi in Sympy [A] time = 2.80194, size = 12, normalized size = 0.6 \[ \frac{2 \left (b x^{n}\right )^{\frac{3}{2}}}{3 n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**n)**(3/2)/x,x)
[Out]
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Mathematica [A] time = 0.0042129, size = 16, normalized size = 0.8 \[ \frac{2 \left (b x^n\right )^{3/2}}{3 n} \]
Antiderivative was successfully verified.
[In] Integrate[(b*x^n)^(3/2)/x,x]
[Out]
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Maple [A] time = 0.002, size = 13, normalized size = 0.7 \[{\frac{2}{3\,n} \left ( b{x}^{n} \right ) ^{{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^n)^(3/2)/x,x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^n)^(3/2)/x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.229261, size = 22, normalized size = 1.1 \[ \frac{2 \, \sqrt{b x^{n}} b x^{n}}{3 \, n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^n)^(3/2)/x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 12.4628, size = 24, normalized size = 1.2 \[ \begin{cases} \frac{2 b^{\frac{3}{2}} \left (x^{n}\right )^{\frac{3}{2}}}{3 n} & \text{for}\: n \neq 0 \\b^{\frac{3}{2}} \log{\left (x \right )} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**n)**(3/2)/x,x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\left (b x^{n}\right )^{\frac{3}{2}}}{x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^n)^(3/2)/x,x, algorithm="giac")
[Out]