Optimal. Leaf size=38 \[ \frac{c^2 (a-b x)^4}{4 b}-\frac{2 a c^2 (a-b x)^3}{3 b} \]
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Rubi [A] time = 0.0455179, antiderivative size = 38, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059 \[ \frac{c^2 (a-b x)^4}{4 b}-\frac{2 a c^2 (a-b x)^3}{3 b} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)*(a*c - b*c*x)^2,x]
[Out]
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Rubi in Sympy [A] time = 11.2217, size = 29, normalized size = 0.76 \[ - \frac{2 a c^{2} \left (a - b x\right )^{3}}{3 b} + \frac{c^{2} \left (a - b x\right )^{4}}{4 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)*(-b*c*x+a*c)**2,x)
[Out]
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Mathematica [A] time = 0.00305104, size = 42, normalized size = 1.11 \[ c^2 \left (a^3 x-\frac{1}{2} a^2 b x^2-\frac{1}{3} a b^2 x^3+\frac{b^3 x^4}{4}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)*(a*c - b*c*x)^2,x]
[Out]
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Maple [A] time = 0.001, size = 45, normalized size = 1.2 \[{\frac{{b}^{3}{c}^{2}{x}^{4}}{4}}-{\frac{a{b}^{2}{c}^{2}{x}^{3}}{3}}-{\frac{{a}^{2}{c}^{2}b{x}^{2}}{2}}+{a}^{3}{c}^{2}x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)*(-b*c*x+a*c)^2,x)
[Out]
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Maxima [A] time = 1.34221, size = 59, normalized size = 1.55 \[ \frac{1}{4} \, b^{3} c^{2} x^{4} - \frac{1}{3} \, a b^{2} c^{2} x^{3} - \frac{1}{2} \, a^{2} b c^{2} x^{2} + a^{3} c^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*c*x - a*c)^2*(b*x + a),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.179143, size = 1, normalized size = 0.03 \[ \frac{1}{4} x^{4} c^{2} b^{3} - \frac{1}{3} x^{3} c^{2} b^{2} a - \frac{1}{2} x^{2} c^{2} b a^{2} + x c^{2} a^{3} \]
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 = 0.116099, size = 46, normalized size = 1.21 \[ a^{3} c^{2} x - \frac{a^{2} b c^{2} x^{2}}{2} - \frac{a b^{2} c^{2} x^{3}}{3} + \frac{b^{3} c^{2} x^{4}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)*(-b*c*x+a*c)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.202387, size = 59, normalized size = 1.55 \[ \frac{1}{4} \, b^{3} c^{2} x^{4} - \frac{1}{3} \, a b^{2} c^{2} x^{3} - \frac{1}{2} \, a^{2} b c^{2} x^{2} + a^{3} c^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*c*x - a*c)^2*(b*x + a),x, algorithm="giac")
[Out]