Optimal. Leaf size=43 \[ \frac{4 a^2 c^2 \log (a+b x)}{b}+\frac{c^2 (a-b x)^2}{2 b}-2 a c^2 x \]
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Rubi [A] time = 0.0410602, antiderivative size = 43, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.053 \[ \frac{4 a^2 c^2 \log (a+b x)}{b}+\frac{c^2 (a-b x)^2}{2 b}-2 a c^2 x \]
Antiderivative was successfully verified.
[In] Int[(a*c - b*c*x)^2/(a + b*x),x]
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Rubi in Sympy [A] time = 11.3474, size = 37, normalized size = 0.86 \[ \frac{4 a^{2} c^{2} \log{\left (a + b x \right )}}{b} - 2 a c^{2} x + \frac{c^{2} \left (a - b x\right )^{2}}{2 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((-b*c*x+a*c)**2/(b*x+a),x)
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Mathematica [A] time = 0.00945582, size = 31, normalized size = 0.72 \[ c^2 \left (\frac{4 a^2 \log (a+b x)}{b}-3 a x+\frac{b x^2}{2}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(a*c - b*c*x)^2/(a + b*x),x]
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Maple [A] time = 0.004, size = 35, normalized size = 0.8 \[{\frac{{c}^{2}b{x}^{2}}{2}}-3\,a{c}^{2}x+4\,{\frac{{a}^{2}{c}^{2}\ln \left ( bx+a \right ) }{b}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((-b*c*x+a*c)^2/(b*x+a),x)
[Out]
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Maxima [A] time = 1.34182, size = 46, normalized size = 1.07 \[ \frac{1}{2} \, b c^{2} x^{2} - 3 \, a c^{2} x + \frac{4 \, a^{2} c^{2} \log \left (b x + a\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*c*x - a*c)^2/(b*x + a),x, algorithm="maxima")
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Fricas [A] time = 0.220068, size = 51, normalized size = 1.19 \[ \frac{b^{2} c^{2} x^{2} - 6 \, a b c^{2} x + 8 \, a^{2} c^{2} \log \left (b x + a\right )}{2 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*c*x - a*c)^2/(b*x + a),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.17284, size = 34, normalized size = 0.79 \[ \frac{4 a^{2} c^{2} \log{\left (a + b x \right )}}{b} - 3 a c^{2} x + \frac{b c^{2} x^{2}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-b*c*x+a*c)**2/(b*x+a),x)
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GIAC/XCAS [A] time = 0.210602, size = 61, normalized size = 1.42 \[ \frac{4 \, a^{2} c^{2}{\rm ln}\left ({\left | b x + a \right |}\right )}{b} + \frac{b^{3} c^{2} x^{2} - 6 \, a b^{2} c^{2} x}{2 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*c*x - a*c)^2/(b*x + a),x, algorithm="giac")
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