Optimal. Leaf size=32 \[ \frac{B \log (a+b x)}{b^2}-\frac{A b-a B}{b^2 (a+b x)} \]
[Out]
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Rubi [A] time = 0.0492553, antiderivative size = 32, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.083 \[ \frac{B \log (a+b x)}{b^2}-\frac{A b-a B}{b^2 (a+b x)} \]
Antiderivative was successfully verified.
[In] Int[(A + B*x)/(a^2 + 2*a*b*x + b^2*x^2),x]
[Out]
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Rubi in Sympy [A] time = 18.0087, size = 26, normalized size = 0.81 \[ \frac{B \log{\left (a + b x \right )}}{b^{2}} - \frac{A b - B a}{b^{2} \left (a + b x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((B*x+A)/(b**2*x**2+2*a*b*x+a**2),x)
[Out]
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Mathematica [A] time = 0.019934, size = 31, normalized size = 0.97 \[ \frac{a B-A b}{b^2 (a+b x)}+\frac{B \log (a+b x)}{b^2} \]
Antiderivative was successfully verified.
[In] Integrate[(A + B*x)/(a^2 + 2*a*b*x + b^2*x^2),x]
[Out]
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Maple [A] time = 0.009, size = 39, normalized size = 1.2 \[{\frac{B\ln \left ( bx+a \right ) }{{b}^{2}}}-{\frac{A}{ \left ( bx+a \right ) b}}+{\frac{Ba}{ \left ( bx+a \right ){b}^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((B*x+A)/(b^2*x^2+2*a*b*x+a^2),x)
[Out]
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Maxima [A] time = 0.686175, size = 46, normalized size = 1.44 \[ \frac{B a - A b}{b^{3} x + a b^{2}} + \frac{B \log \left (b x + a\right )}{b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)/(b^2*x^2 + 2*a*b*x + a^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.280507, size = 50, normalized size = 1.56 \[ \frac{B a - A b +{\left (B b x + B a\right )} \log \left (b x + a\right )}{b^{3} x + a b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)/(b^2*x^2 + 2*a*b*x + a^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.47882, size = 27, normalized size = 0.84 \[ \frac{B \log{\left (a + b x \right )}}{b^{2}} + \frac{- A b + B a}{a b^{2} + b^{3} x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x+A)/(b**2*x**2+2*a*b*x+a**2),x)
[Out]
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GIAC/XCAS [A] time = 0.26842, size = 43, normalized size = 1.34 \[ \frac{B{\rm ln}\left ({\left | b x + a \right |}\right )}{b^{2}} + \frac{B a - A b}{{\left (b x + a\right )} b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)/(b^2*x^2 + 2*a*b*x + a^2),x, algorithm="giac")
[Out]