Optimal. Leaf size=24 \[ \frac{\sqrt{a^2+2 a b x+b^2 x^2}}{b} \]
[Out]
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Rubi [A] time = 0.013966, antiderivative size = 24, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 26, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.038 \[ \frac{\sqrt{a^2+2 a b x+b^2 x^2}}{b} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]
[Out]
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Rubi in Sympy [A] time = 2.49171, size = 10, normalized size = 0.42 \[ \frac{\sqrt{\left (a + b x\right )^{2}}}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)/((b*x+a)**2)**(1/2),x)
[Out]
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Mathematica [A] time = 0.00816341, size = 18, normalized size = 0.75 \[ \frac{x (a+b x)}{\sqrt{(a+b x)^2}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]
[Out]
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Maple [A] time = 0.002, size = 17, normalized size = 0.7 \[{ \left ( bx+a \right ) x{\frac{1}{\sqrt{ \left ( bx+a \right ) ^{2}}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)/((b*x+a)^2)^(1/2),x)
[Out]
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Maxima [A] time = 0.687061, size = 18, normalized size = 0.75 \[ \frac{\sqrt{{\left (b x + a\right )}^{2}}}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)/sqrt((b*x + a)^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.274946, size = 1, normalized size = 0.04 \[ x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)/sqrt((b*x + a)^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.136042, size = 0, normalized size = 0. \[ x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)/((b*x+a)**2)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.275021, size = 27, normalized size = 1.12 \[ x{\rm sign}\left (b x + a\right ) + \frac{a{\rm sign}\left (b x + a\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)/sqrt((b*x + a)^2),x, algorithm="giac")
[Out]