Optimal. Leaf size=61 \[ \frac{8 a^3 c^3 \log (a+b x)}{b}-4 a^2 c^3 x+\frac{c^3 (a-b x)^3}{3 b}+\frac{a c^3 (a-b x)^2}{b} \]
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Rubi [A] time = 0.0536301, antiderivative size = 61, 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 \[ \frac{8 a^3 c^3 \log (a+b x)}{b}-4 a^2 c^3 x+\frac{c^3 (a-b x)^3}{3 b}+\frac{a c^3 (a-b x)^2}{b} \]
Antiderivative was successfully verified.
[In] Int[(a*c - b*c*x)^3/(a + b*x),x]
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Rubi in Sympy [A] time = 14.9552, size = 53, normalized size = 0.87 \[ \frac{8 a^{3} c^{3} \log{\left (a + b x \right )}}{b} - 4 a^{2} c^{3} x + \frac{a c^{3} \left (a - b x\right )^{2}}{b} + \frac{c^{3} \left (a - b x\right )^{3}}{3 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((-b*c*x+a*c)**3/(b*x+a),x)
[Out]
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Mathematica [A] time = 0.010585, size = 42, normalized size = 0.69 \[ c^3 \left (\frac{8 a^3 \log (a+b x)}{b}-7 a^2 x+2 a b x^2-\frac{b^2 x^3}{3}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(a*c - b*c*x)^3/(a + b*x),x]
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Maple [A] time = 0.004, size = 49, normalized size = 0.8 \[ -{\frac{{c}^{3}{b}^{2}{x}^{3}}{3}}+2\,{c}^{3}b{x}^{2}a-7\,{a}^{2}{c}^{3}x+8\,{\frac{{a}^{3}{c}^{3}\ln \left ( bx+a \right ) }{b}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((-b*c*x+a*c)^3/(b*x+a),x)
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Maxima [A] time = 1.3436, size = 65, normalized size = 1.07 \[ -\frac{1}{3} \, b^{2} c^{3} x^{3} + 2 \, a b c^{3} x^{2} - 7 \, a^{2} c^{3} x + \frac{8 \, a^{3} c^{3} \log \left (b x + a\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^3/(b*x + a),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.217258, size = 70, normalized size = 1.15 \[ -\frac{b^{3} c^{3} x^{3} - 6 \, a b^{2} c^{3} x^{2} + 21 \, a^{2} b c^{3} x - 24 \, a^{3} c^{3} \log \left (b x + a\right )}{3 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^3/(b*x + a),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.28158, size = 49, normalized size = 0.8 \[ \frac{8 a^{3} c^{3} \log{\left (a + b x \right )}}{b} - 7 a^{2} c^{3} x + 2 a b c^{3} x^{2} - \frac{b^{2} c^{3} x^{3}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-b*c*x+a*c)**3/(b*x+a),x)
[Out]
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GIAC/XCAS [A] time = 0.205888, size = 80, normalized size = 1.31 \[ \frac{8 \, a^{3} c^{3}{\rm ln}\left ({\left | b x + a \right |}\right )}{b} - \frac{b^{5} c^{3} x^{3} - 6 \, a b^{4} c^{3} x^{2} + 21 \, a^{2} b^{3} c^{3} x}{3 \, b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^3/(b*x + a),x, algorithm="giac")
[Out]