Optimal. Leaf size=41 \[ -\frac{2 a A}{3 x^{3/2}}-\frac{2 a B}{\sqrt{x}}+2 A c \sqrt{x}+\frac{2}{3} B c x^{3/2} \]
[Out]
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Rubi [A] time = 0.0415767, antiderivative size = 41, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056 \[ -\frac{2 a A}{3 x^{3/2}}-\frac{2 a B}{\sqrt{x}}+2 A c \sqrt{x}+\frac{2}{3} B c x^{3/2} \]
Antiderivative was successfully verified.
[In] Int[((A + B*x)*(a + c*x^2))/x^(5/2),x]
[Out]
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Rubi in Sympy [A] time = 5.0343, size = 42, normalized size = 1.02 \[ - \frac{2 A a}{3 x^{\frac{3}{2}}} + 2 A c \sqrt{x} - \frac{2 B a}{\sqrt{x}} + \frac{2 B c x^{\frac{3}{2}}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((B*x+A)*(c*x**2+a)/x**(5/2),x)
[Out]
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Mathematica [A] time = 0.01884, size = 32, normalized size = 0.78 \[ \frac{2 c x^2 (3 A+B x)-2 a (A+3 B x)}{3 x^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[((A + B*x)*(a + c*x^2))/x^(5/2),x]
[Out]
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Maple [A] time = 0.006, size = 29, normalized size = 0.7 \[ -{\frac{-2\,Bc{x}^{3}-6\,Ac{x}^{2}+6\,aBx+2\,aA}{3}{x}^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((B*x+A)*(c*x^2+a)/x^(5/2),x)
[Out]
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Maxima [A] time = 0.68074, size = 39, normalized size = 0.95 \[ \frac{2}{3} \, B c x^{\frac{3}{2}} + 2 \, A c \sqrt{x} - \frac{2 \,{\left (3 \, B a x + A a\right )}}{3 \, x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + a)*(B*x + A)/x^(5/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.286121, size = 38, normalized size = 0.93 \[ \frac{2 \,{\left (B c x^{3} + 3 \, A c x^{2} - 3 \, B a x - A a\right )}}{3 \, x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + a)*(B*x + A)/x^(5/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.18323, size = 42, normalized size = 1.02 \[ - \frac{2 A a}{3 x^{\frac{3}{2}}} + 2 A c \sqrt{x} - \frac{2 B a}{\sqrt{x}} + \frac{2 B c x^{\frac{3}{2}}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x+A)*(c*x**2+a)/x**(5/2),x)
[Out]
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GIAC/XCAS [A] time = 0.27904, size = 39, normalized size = 0.95 \[ \frac{2}{3} \, B c x^{\frac{3}{2}} + 2 \, A c \sqrt{x} - \frac{2 \,{\left (3 \, B a x + A a\right )}}{3 \, x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + a)*(B*x + A)/x^(5/2),x, algorithm="giac")
[Out]