Optimal. Leaf size=35 \[ \frac{(a+b x) \log (a+b x)}{b \sqrt{a^2+2 a b x+b^2 x^2}} \]
[Out]
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Rubi [A] time = 0.0254914, antiderivative size = 35, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1 \[ \frac{(a+b x) \log (a+b x)}{b \sqrt{a^2+2 a b x+b^2 x^2}} \]
Antiderivative was successfully verified.
[In] Int[1/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]
[Out]
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Rubi in Sympy [A] time = 3.06716, size = 32, normalized size = 0.91 \[ \frac{\left (a + b x\right ) \log{\left (a + b x \right )}}{b \sqrt{a^{2} + 2 a b x + b^{2} x^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/((b*x+a)**2)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0134335, size = 26, normalized size = 0.74 \[ \frac{(a+b x) \log (a+b x)}{b \sqrt{(a+b x)^2}} \]
Antiderivative was successfully verified.
[In] Integrate[1/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]
[Out]
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Maple [A] time = 0.005, size = 25, normalized size = 0.7 \[{\frac{ \left ( bx+a \right ) \ln \left ( bx+a \right ) }{b}{\frac{1}{\sqrt{ \left ( bx+a \right ) ^{2}}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/((b*x+a)^2)^(1/2),x)
[Out]
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Maxima [A] time = 0.718246, size = 19, normalized size = 0.54 \[ \sqrt{\frac{1}{b^{2}}} \log \left (x + \frac{a}{b}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt((b*x + a)^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.217344, size = 14, normalized size = 0.4 \[ \frac{\log \left (b x + a\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt((b*x + a)^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.141737, size = 7, normalized size = 0.2 \[ \frac{\log{\left (a + b x \right )}}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x+a)**2)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.205192, size = 23, normalized size = 0.66 \[ \frac{{\rm ln}\left ({\left | b x + a \right |}\right ){\rm sign}\left (b x + a\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt((b*x + a)^2),x, algorithm="giac")
[Out]