Optimal. Leaf size=37 \[ -\frac{2 (a B+A b)}{3 x^{3/2}}-\frac{2 a A}{5 x^{5/2}}-\frac{2 b B}{\sqrt{x}} \]
[Out]
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Rubi [A] time = 0.0501797, antiderivative size = 37, 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 \[ -\frac{2 (a B+A b)}{3 x^{3/2}}-\frac{2 a A}{5 x^{5/2}}-\frac{2 b B}{\sqrt{x}} \]
Antiderivative was successfully verified.
[In] Int[((a + b*x)*(A + B*x))/x^(7/2),x]
[Out]
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Rubi in Sympy [A] time = 5.29976, size = 41, normalized size = 1.11 \[ - \frac{2 A a}{5 x^{\frac{5}{2}}} - \frac{2 B b}{\sqrt{x}} - \frac{\frac{2 A b}{3} + \frac{2 B a}{3}}{x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)*(B*x+A)/x**(7/2),x)
[Out]
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Mathematica [A] time = 0.0157182, size = 30, normalized size = 0.81 \[ -\frac{2 (a (3 A+5 B x)+5 b x (A+3 B x))}{15 x^{5/2}} \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x)*(A + B*x))/x^(7/2),x]
[Out]
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Maple [A] time = 0.006, size = 28, normalized size = 0.8 \[ -{\frac{30\,bB{x}^{2}+10\,Abx+10\,Bax+6\,Aa}{15}{x}^{-{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)*(B*x+A)/x^(7/2),x)
[Out]
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Maxima [A] time = 1.33285, size = 36, normalized size = 0.97 \[ -\frac{2 \,{\left (15 \, B b x^{2} + 3 \, A a + 5 \,{\left (B a + A b\right )} x\right )}}{15 \, x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)/x^(7/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.20682, size = 36, normalized size = 0.97 \[ -\frac{2 \,{\left (15 \, B b x^{2} + 3 \, A a + 5 \,{\left (B a + A b\right )} x\right )}}{15 \, x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)/x^(7/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 7.60234, size = 46, normalized size = 1.24 \[ - \frac{2 A a}{5 x^{\frac{5}{2}}} - \frac{2 A b}{3 x^{\frac{3}{2}}} - \frac{2 B a}{3 x^{\frac{3}{2}}} - \frac{2 B b}{\sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)*(B*x+A)/x**(7/2),x)
[Out]
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GIAC/XCAS [A] time = 0.262276, size = 36, normalized size = 0.97 \[ -\frac{2 \,{\left (15 \, B b x^{2} + 5 \, B a x + 5 \, A b x + 3 \, A a\right )}}{15 \, x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)/x^(7/2),x, algorithm="giac")
[Out]