Optimal. Leaf size=28 \[ -\frac{4 a^2 \log (a-b x)}{b}-3 a x-\frac{b x^2}{2} \]
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Rubi [A] time = 0.0404711, antiderivative size = 28, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ -\frac{4 a^2 \log (a-b x)}{b}-3 a x-\frac{b x^2}{2} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)^3/(a^2 - b^2*x^2),x]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{4 a^{2} \log{\left (a - b x \right )}}{b} - 3 a x - b \int x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**3/(-b**2*x**2+a**2),x)
[Out]
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Mathematica [A] time = 0.00933326, size = 28, normalized size = 1. \[ -\frac{4 a^2 \log (a-b x)}{b}-3 a x-\frac{b x^2}{2} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)^3/(a^2 - b^2*x^2),x]
[Out]
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Maple [A] time = 0.005, size = 28, normalized size = 1. \[ -{\frac{b{x}^{2}}{2}}-3\,ax-4\,{\frac{{a}^{2}\ln \left ( bx-a \right ) }{b}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^3/(-b^2*x^2+a^2),x)
[Out]
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Maxima [A] time = 0.689342, size = 36, normalized size = 1.29 \[ -\frac{1}{2} \, b x^{2} - 3 \, a x - \frac{4 \, a^{2} \log \left (b x - a\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*x + a)^3/(b^2*x^2 - a^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.208629, size = 42, normalized size = 1.5 \[ -\frac{b^{2} x^{2} + 6 \, a b x + 8 \, a^{2} \log \left (b x - a\right )}{2 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*x + a)^3/(b^2*x^2 - a^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.19004, size = 26, normalized size = 0.93 \[ - \frac{4 a^{2} \log{\left (- a + b x \right )}}{b} - 3 a x - \frac{b x^{2}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)**3/(-b**2*x**2+a**2),x)
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GIAC/XCAS [A] time = 0.215774, size = 51, normalized size = 1.82 \[ -\frac{4 \, a^{2}{\rm ln}\left ({\left | b x - a \right |}\right )}{b} - \frac{b^{3} x^{2} + 6 \, a b^{2} x}{2 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*x + a)^3/(b^2*x^2 - a^2),x, algorithm="giac")
[Out]