Optimal. Leaf size=14 \[ \frac{(a+b x)^6}{6 b} \]
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Rubi [A] time = 0.00869202, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.083 \[ \frac{(a+b x)^6}{6 b} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^2,x]
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Rubi in Sympy [A] time = 9.47501, size = 8, normalized size = 0.57 \[ \frac{\left (a + b x\right )^{6}}{6 b} \]
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)**2,x)
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Mathematica [A] time = 0.0034795, size = 14, normalized size = 1. \[ \frac{(a+b x)^6}{6 b} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^2,x]
[Out]
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Maple [B] time = 0.002, size = 54, normalized size = 3.9 \[{\frac{{b}^{5}{x}^{6}}{6}}+a{b}^{4}{x}^{5}+{\frac{5\,{a}^{2}{b}^{3}{x}^{4}}{2}}+{\frac{10\,{a}^{3}{b}^{2}{x}^{3}}{3}}+{\frac{5\,{a}^{4}b{x}^{2}}{2}}+{a}^{5}x \]
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)^2,x)
[Out]
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Maxima [A] time = 0.710033, size = 31, normalized size = 2.21 \[ \frac{{\left (b^{2} x^{2} + 2 \, a b x + a^{2}\right )}^{3}}{6 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^2 + 2*a*b*x + a^2)^2*(b*x + a),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.254799, size = 1, normalized size = 0.07 \[ \frac{1}{6} x^{6} b^{5} + x^{5} b^{4} a + \frac{5}{2} x^{4} b^{3} a^{2} + \frac{10}{3} x^{3} b^{2} a^{3} + \frac{5}{2} x^{2} b a^{4} + x a^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^2 + 2*a*b*x + a^2)^2*(b*x + a),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.1257, size = 60, normalized size = 4.29 \[ a^{5} x + \frac{5 a^{4} b x^{2}}{2} + \frac{10 a^{3} b^{2} x^{3}}{3} + \frac{5 a^{2} b^{3} x^{4}}{2} + a b^{4} x^{5} + \frac{b^{5} x^{6}}{6} \]
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)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.271114, size = 72, normalized size = 5.14 \[ \frac{1}{6} \, b^{5} x^{6} + a b^{4} x^{5} + \frac{5}{2} \, a^{2} b^{3} x^{4} + \frac{10}{3} \, a^{3} b^{2} x^{3} + \frac{5}{2} \, a^{4} b x^{2} + a^{5} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^2 + 2*a*b*x + a^2)^2*(b*x + a),x, algorithm="giac")
[Out]