Optimal. Leaf size=61 \[ \frac{(a+b x)^5 (A b-2 a B)}{5 b^3}-\frac{a (a+b x)^4 (A b-a B)}{4 b^3}+\frac{B (a+b x)^6}{6 b^3} \]
[Out]
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Rubi [A] time = 0.10964, antiderivative size = 61, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.071 \[ \frac{(a+b x)^5 (A b-2 a B)}{5 b^3}-\frac{a (a+b x)^4 (A b-a B)}{4 b^3}+\frac{B (a+b x)^6}{6 b^3} \]
Antiderivative was successfully verified.
[In] Int[x*(a + b*x)^3*(A + B*x),x]
[Out]
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Rubi in Sympy [A] time = 24.0858, size = 53, normalized size = 0.87 \[ \frac{B \left (a + b x\right )^{6}}{6 b^{3}} - \frac{a \left (a + b x\right )^{4} \left (A b - B a\right )}{4 b^{3}} + \frac{\left (a + b x\right )^{5} \left (A b - 2 B a\right )}{5 b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*(b*x+a)**3*(B*x+A),x)
[Out]
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Mathematica [A] time = 0.020963, size = 69, normalized size = 1.13 \[ \frac{1}{60} x^2 \left (10 a^3 (3 A+2 B x)+15 a^2 b x (4 A+3 B x)+9 a b^2 x^2 (5 A+4 B x)+2 b^3 x^3 (6 A+5 B x)\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x*(a + b*x)^3*(A + B*x),x]
[Out]
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Maple [A] time = 0.002, size = 76, normalized size = 1.3 \[{\frac{{b}^{3}B{x}^{6}}{6}}+{\frac{ \left ({b}^{3}A+3\,a{b}^{2}B \right ){x}^{5}}{5}}+{\frac{ \left ( 3\,a{b}^{2}A+3\,{a}^{2}bB \right ){x}^{4}}{4}}+{\frac{ \left ( 3\,{a}^{2}bA+{a}^{3}B \right ){x}^{3}}{3}}+{\frac{{a}^{3}A{x}^{2}}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*(b*x+a)^3*(B*x+A),x)
[Out]
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Maxima [A] time = 1.33746, size = 99, normalized size = 1.62 \[ \frac{1}{6} \, B b^{3} x^{6} + \frac{1}{2} \, A a^{3} x^{2} + \frac{1}{5} \,{\left (3 \, B a b^{2} + A b^{3}\right )} x^{5} + \frac{3}{4} \,{\left (B a^{2} b + A a b^{2}\right )} x^{4} + \frac{1}{3} \,{\left (B a^{3} + 3 \, A a^{2} b\right )} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^3*x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.180292, size = 1, normalized size = 0.02 \[ \frac{1}{6} x^{6} b^{3} B + \frac{3}{5} x^{5} b^{2} a B + \frac{1}{5} x^{5} b^{3} A + \frac{3}{4} x^{4} b a^{2} B + \frac{3}{4} x^{4} b^{2} a A + \frac{1}{3} x^{3} a^{3} B + x^{3} b a^{2} A + \frac{1}{2} x^{2} a^{3} A \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^3*x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.155511, size = 80, normalized size = 1.31 \[ \frac{A a^{3} x^{2}}{2} + \frac{B b^{3} x^{6}}{6} + x^{5} \left (\frac{A b^{3}}{5} + \frac{3 B a b^{2}}{5}\right ) + x^{4} \left (\frac{3 A a b^{2}}{4} + \frac{3 B a^{2} b}{4}\right ) + x^{3} \left (A a^{2} b + \frac{B a^{3}}{3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*(b*x+a)**3*(B*x+A),x)
[Out]
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GIAC/XCAS [A] time = 0.262637, size = 103, normalized size = 1.69 \[ \frac{1}{6} \, B b^{3} x^{6} + \frac{3}{5} \, B a b^{2} x^{5} + \frac{1}{5} \, A b^{3} x^{5} + \frac{3}{4} \, B a^{2} b x^{4} + \frac{3}{4} \, A a b^{2} x^{4} + \frac{1}{3} \, B a^{3} x^{3} + A a^{2} b x^{3} + \frac{1}{2} \, A a^{3} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^3*x,x, algorithm="giac")
[Out]