Optimal. Leaf size=30 \[ \frac{a x^{m+1}}{m+1}+\frac{2 b x^{m+\frac{3}{2}}}{2 m+3} \]
[Out]
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Rubi [A] time = 0.0242294, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{a x^{m+1}}{m+1}+\frac{2 b x^{m+\frac{3}{2}}}{2 m+3} \]
Antiderivative was successfully verified.
[In] Int[(a + b*Sqrt[x])*x^m,x]
[Out]
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Rubi in Sympy [A] time = 4.46858, size = 24, normalized size = 0.8 \[ \frac{a x^{m + 1}}{m + 1} + \frac{2 b x^{m + \frac{3}{2}}}{2 m + 3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**m*(a+b*x**(1/2)),x)
[Out]
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Mathematica [A] time = 0.0412618, size = 28, normalized size = 0.93 \[ x^m \left (\frac{a x}{m+1}+\frac{2 b x^{3/2}}{2 m+3}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*Sqrt[x])*x^m,x]
[Out]
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Maple [F] time = 0.007, size = 0, normalized size = 0. \[ \int{x}^{m} \left ( a+b\sqrt{x} \right ) \, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^m*(a+b*x^(1/2)),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*sqrt(x) + a)*x^m,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.254054, size = 50, normalized size = 1.67 \[ \frac{{\left (2 \,{\left (b m + b\right )} x^{\frac{3}{2}} +{\left (2 \, a m + 3 \, a\right )} x\right )} x^{m}}{2 \, m^{2} + 5 \, m + 3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)*x^m,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**m*(a+b*x**(1/2)),x)
[Out]
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GIAC/XCAS [A] time = 0.269757, size = 51, normalized size = 1.7 \[ \frac{2 \, b x^{\frac{3}{2}} e^{\left (2 \, m{\rm ln}\left (\sqrt{x}\right )\right )}}{2 \, m + 3} + \frac{a x e^{\left (2 \, m{\rm ln}\left (\sqrt{x}\right )\right )}}{m + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)*x^m,x, algorithm="giac")
[Out]