Optimal. Leaf size=51 \[ -\frac{2 (a B+A b)}{\sqrt{x}}-\frac{2 a A}{3 x^{3/2}}+2 \sqrt{x} (A c+b B)+\frac{2}{3} B c x^{3/2} \]
[Out]
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Rubi [A] time = 0.0665046, antiderivative size = 51, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.048 \[ -\frac{2 (a B+A b)}{\sqrt{x}}-\frac{2 a A}{3 x^{3/2}}+2 \sqrt{x} (A c+b B)+\frac{2}{3} B c x^{3/2} \]
Antiderivative was successfully verified.
[In] Int[((A + B*x)*(a + b*x + c*x^2))/x^(5/2),x]
[Out]
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Rubi in Sympy [A] time = 8.40281, size = 53, normalized size = 1.04 \[ - \frac{2 A a}{3 x^{\frac{3}{2}}} + \frac{2 B c x^{\frac{3}{2}}}{3} + \sqrt{x} \left (2 A c + 2 B b\right ) - \frac{2 A b + 2 B a}{\sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((B*x+A)*(c*x**2+b*x+a)/x**(5/2),x)
[Out]
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Mathematica [A] time = 0.0294311, size = 42, normalized size = 0.82 \[ \frac{2 x (B x (3 b+c x)-3 A (b-c x))-2 a (A+3 B x)}{3 x^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[((A + B*x)*(a + b*x + c*x^2))/x^(5/2),x]
[Out]
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Maple [A] time = 0.006, size = 41, normalized size = 0.8 \[ -{\frac{-2\,Bc{x}^{3}-6\,Ac{x}^{2}-6\,Bb{x}^{2}+6\,Abx+6\,aBx+2\,aA}{3}{x}^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((B*x+A)*(c*x^2+b*x+a)/x^(5/2),x)
[Out]
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Maxima [A] time = 0.715795, size = 53, normalized size = 1.04 \[ \frac{2}{3} \, B c x^{\frac{3}{2}} + 2 \,{\left (B b + A c\right )} \sqrt{x} - \frac{2 \,{\left (A a + 3 \,{\left (B a + A b\right )} x\right )}}{3 \, x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)*(B*x + A)/x^(5/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.274365, size = 51, normalized size = 1. \[ \frac{2 \,{\left (B c x^{3} + 3 \,{\left (B b + A c\right )} x^{2} - A a - 3 \,{\left (B a + A b\right )} x\right )}}{3 \, x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)*(B*x + A)/x^(5/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.42229, size = 63, normalized size = 1.24 \[ - \frac{2 A a}{3 x^{\frac{3}{2}}} - \frac{2 A b}{\sqrt{x}} + 2 A c \sqrt{x} - \frac{2 B a}{\sqrt{x}} + 2 B b \sqrt{x} + \frac{2 B c x^{\frac{3}{2}}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x+A)*(c*x**2+b*x+a)/x**(5/2),x)
[Out]
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GIAC/XCAS [A] time = 0.27182, size = 55, normalized size = 1.08 \[ \frac{2}{3} \, B c x^{\frac{3}{2}} + 2 \, B b \sqrt{x} + 2 \, A c \sqrt{x} - \frac{2 \,{\left (3 \, B a x + 3 \, A b x + A a\right )}}{3 \, x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)*(B*x + A)/x^(5/2),x, algorithm="giac")
[Out]