Optimal. Leaf size=24 \[ \frac{2 b x^{n+2} \sqrt{b x^n}}{3 n+4} \]
[Out]
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Rubi [A] time = 0.017304, antiderivative size = 24, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182 \[ \frac{2 b x^{n+2} \sqrt{b x^n}}{3 n+4} \]
Antiderivative was successfully verified.
[In] Int[x*(b*x^n)^(3/2),x]
[Out]
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Rubi in Sympy [A] time = 2.95375, size = 29, normalized size = 1.21 \[ \frac{2 b x^{- \frac{n}{2}} x^{\frac{3 n}{2} + 2} \sqrt{b x^{n}}}{3 n + 4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*(b*x**n)**(3/2),x)
[Out]
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Mathematica [A] time = 0.00963597, size = 22, normalized size = 0.92 \[ \frac{x^2 \left (b x^n\right )^{3/2}}{\frac{3 n}{2}+2} \]
Antiderivative was successfully verified.
[In] Integrate[x*(b*x^n)^(3/2),x]
[Out]
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Maple [A] time = 0.004, size = 20, normalized size = 0.8 \[ 2\,{\frac{{x}^{2} \left ( b{x}^{n} \right ) ^{3/2}}{4+3\,n}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*(b*x^n)^(3/2),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 [F(-2)] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: TypeError} \]
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 [F(-2)] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: TypeError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*(b*x**n)**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.229467, size = 28, normalized size = 1.17 \[ \frac{2 \, b^{\frac{3}{2}} x^{2} e^{\left (\frac{3}{2} \, n{\rm ln}\left (x\right )\right )}}{3 \, n + 4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^n)^(3/2)*x,x, algorithm="giac")
[Out]