Optimal. Leaf size=24 \[ \frac{2 x^{m+1} \sqrt{b x^n}}{2 m+n+2} \]
[Out]
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Rubi [A] time = 0.017473, antiderivative size = 24, 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 \[ \frac{2 x^{m+1} \sqrt{b x^n}}{2 m+n+2} \]
Antiderivative was successfully verified.
[In] Int[x^m*Sqrt[b*x^n],x]
[Out]
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Rubi in Sympy [A] time = 3.38072, size = 29, normalized size = 1.21 \[ \frac{2 x^{- \frac{n}{2}} x^{m + \frac{n}{2} + 1} \sqrt{b x^{n}}}{2 m + n + 2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**m*(b*x**n)**(1/2),x)
[Out]
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Mathematica [A] time = 0.00817237, size = 25, normalized size = 1.04 \[ \frac{x^{m+1} \sqrt{b x^n}}{m+\frac{n}{2}+1} \]
Antiderivative was successfully verified.
[In] Integrate[x^m*Sqrt[b*x^n],x]
[Out]
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Maple [A] time = 0.003, size = 23, normalized size = 1. \[ 2\,{\frac{{x}^{1+m}\sqrt{b{x}^{n}}}{2+2\,m+n}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^m*(b*x^n)^(1/2),x)
[Out]
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Maxima [A] time = 1.45467, size = 30, normalized size = 1.25 \[ \frac{2 \, \sqrt{b} x x^{m} \sqrt{x^{n}}}{2 \, m + n + 2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b*x^n)*x^m,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(sqrt(b*x^n)*x^m,x, algorithm="fricas")
[Out]
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**m*(b*x**n)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.227212, size = 34, normalized size = 1.42 \[ \frac{2 \, \sqrt{b} x e^{\left (m{\rm ln}\left (x\right ) + \frac{1}{2} \, n{\rm ln}\left (x\right )\right )}}{2 \, m + n + 2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b*x^n)*x^m,x, algorithm="giac")
[Out]