Optimal. Leaf size=35 \[ -\frac{2 (a B+A b)}{\sqrt{x}}-\frac{2 a A}{3 x^{3/2}}+2 b B \sqrt{x} \]
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Rubi [A] time = 0.0427225, antiderivative size = 35, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062 \[ -\frac{2 (a B+A b)}{\sqrt{x}}-\frac{2 a A}{3 x^{3/2}}+2 b B \sqrt{x} \]
Antiderivative was successfully verified.
[In] Int[((a + b*x)*(A + B*x))/x^(5/2),x]
[Out]
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Rubi in Sympy [A] time = 5.21823, size = 36, normalized size = 1.03 \[ - \frac{2 A a}{3 x^{\frac{3}{2}}} + 2 B b \sqrt{x} - \frac{2 A b + 2 B a}{\sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)*(B*x+A)/x**(5/2),x)
[Out]
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Mathematica [A] time = 0.0150795, size = 28, normalized size = 0.8 \[ -\frac{2 (a (A+3 B x)+3 b x (A-B x))}{3 x^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x)*(A + B*x))/x^(5/2),x]
[Out]
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Maple [A] time = 0.006, size = 27, normalized size = 0.8 \[ -{\frac{-6\,bB{x}^{2}+6\,Abx+6\,Bax+2\,Aa}{3}{x}^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)*(B*x+A)/x^(5/2),x)
[Out]
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Maxima [A] time = 1.3415, size = 36, normalized size = 1.03 \[ 2 \, B b \sqrt{x} - \frac{2 \,{\left (A a + 3 \,{\left (B a + A b\right )} x\right )}}{3 \, x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)/x^(5/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.206176, size = 36, normalized size = 1.03 \[ \frac{2 \,{\left (3 \, B b x^{2} - A a - 3 \,{\left (B a + A b\right )} x\right )}}{3 \, x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)/x^(5/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.64516, size = 41, normalized size = 1.17 \[ - \frac{2 A a}{3 x^{\frac{3}{2}}} - \frac{2 A b}{\sqrt{x}} - \frac{2 B a}{\sqrt{x}} + 2 B b \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)*(B*x+A)/x**(5/2),x)
[Out]
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GIAC/XCAS [A] time = 0.257555, size = 36, normalized size = 1.03 \[ 2 \, B b \sqrt{x} - \frac{2 \,{\left (3 \, B a x + 3 \, A b x + A a\right )}}{3 \, x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)/x^(5/2),x, algorithm="giac")
[Out]