Optimal. Leaf size=37 \[ \frac{2}{3} x^{3/2} (a B+A b)+2 a A \sqrt{x}+\frac{2}{5} b B x^{5/2} \]
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Rubi [A] time = 0.0422918, 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 \[ \frac{2}{3} x^{3/2} (a B+A b)+2 a A \sqrt{x}+\frac{2}{5} b B x^{5/2} \]
Antiderivative was successfully verified.
[In] Int[((a + b*x)*(A + B*x))/Sqrt[x],x]
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Rubi in Sympy [A] time = 5.31753, size = 39, normalized size = 1.05 \[ 2 A a \sqrt{x} + \frac{2 B b x^{\frac{5}{2}}}{5} + x^{\frac{3}{2}} \left (\frac{2 A b}{3} + \frac{2 B a}{3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)*(B*x+A)/x**(1/2),x)
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Mathematica [A] time = 0.0153496, size = 31, normalized size = 0.84 \[ \frac{2}{15} \sqrt{x} (5 a (3 A+B x)+b x (5 A+3 B x)) \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x)*(A + B*x))/Sqrt[x],x]
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Maple [A] time = 0.006, size = 28, normalized size = 0.8 \[{\frac{6\,bB{x}^{2}+10\,Abx+10\,Bax+30\,Aa}{15}\sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)*(B*x+A)/x^(1/2),x)
[Out]
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Maxima [A] time = 1.32874, size = 36, normalized size = 0.97 \[ \frac{2}{5} \, B b x^{\frac{5}{2}} + 2 \, A a \sqrt{x} + \frac{2}{3} \,{\left (B a + A b\right )} x^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)/sqrt(x),x, algorithm="maxima")
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Fricas [A] time = 0.206699, size = 36, normalized size = 0.97 \[ \frac{2}{15} \,{\left (3 \, B b x^{2} + 15 \, A a + 5 \,{\left (B a + A b\right )} x\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)/sqrt(x),x, algorithm="fricas")
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Sympy [A] time = 5.04412, size = 44, normalized size = 1.19 \[ 2 A a \sqrt{x} + \frac{2 A b x^{\frac{3}{2}}}{3} + \frac{2 B a x^{\frac{3}{2}}}{3} + \frac{2 B b x^{\frac{5}{2}}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)*(B*x+A)/x**(1/2),x)
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GIAC/XCAS [A] time = 0.261892, size = 39, normalized size = 1.05 \[ \frac{2}{5} \, B b x^{\frac{5}{2}} + \frac{2}{3} \, B a x^{\frac{3}{2}} + \frac{2}{3} \, A b x^{\frac{3}{2}} + 2 \, A a \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)/sqrt(x),x, algorithm="giac")
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