Optimal. Leaf size=38 \[ \frac{(a+b x)^5 (A b-a B)}{5 b^2}+\frac{B (a+b x)^6}{6 b^2} \]
[Out]
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Rubi [A] time = 0.0465988, antiderivative size = 38, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.083 \[ \frac{(a+b x)^5 (A b-a B)}{5 b^2}+\frac{B (a+b x)^6}{6 b^2} \]
Antiderivative was successfully verified.
[In] Int[(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2,x]
[Out]
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Rubi in Sympy [A] time = 22.4607, size = 31, normalized size = 0.82 \[ \frac{B \left (a + b x\right )^{6}}{6 b^{2}} + \frac{\left (a + b x\right )^{5} \left (A b - B a\right )}{5 b^{2}} \]
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)
[Out]
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Mathematica [B] time = 0.03167, size = 84, normalized size = 2.21 \[ \frac{1}{30} x \left (15 a^4 (2 A+B x)+20 a^3 b x (3 A+2 B x)+15 a^2 b^2 x^2 (4 A+3 B x)+6 a b^3 x^3 (5 A+4 B x)+b^4 x^4 (6 A+5 B x)\right ) \]
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 = 0.001, size = 97, normalized size = 2.6 \[{\frac{{b}^{4}B{x}^{6}}{6}}+{\frac{ \left ( A{b}^{4}+4\,Ba{b}^{3} \right ){x}^{5}}{5}}+{\frac{ \left ( 4\,Aa{b}^{3}+6\,{b}^{2}B{a}^{2} \right ){x}^{4}}{4}}+{\frac{ \left ( 6\,A{a}^{2}{b}^{2}+4\,{a}^{3}bB \right ){x}^{3}}{3}}+{\frac{ \left ( 4\,A{a}^{3}b+B{a}^{4} \right ){x}^{2}}{2}}+{a}^{4}Ax \]
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 = 0.69452, size = 130, normalized size = 3.42 \[ \frac{1}{6} \, B b^{4} x^{6} + A a^{4} x + \frac{1}{5} \,{\left (4 \, B a b^{3} + A b^{4}\right )} x^{5} + \frac{1}{2} \,{\left (3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right )} x^{4} + \frac{2}{3} \,{\left (2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right )} x^{3} + \frac{1}{2} \,{\left (B a^{4} + 4 \, A a^{3} b\right )} x^{2} \]
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 = 0.248597, size = 1, normalized size = 0.03 \[ \frac{1}{6} x^{6} b^{4} B + \frac{4}{5} x^{5} b^{3} a B + \frac{1}{5} x^{5} b^{4} A + \frac{3}{2} x^{4} b^{2} a^{2} B + x^{4} b^{3} a A + \frac{4}{3} x^{3} b a^{3} B + 2 x^{3} b^{2} a^{2} A + \frac{1}{2} x^{2} a^{4} B + 2 x^{2} b a^{3} A + x a^{4} A \]
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 = 0.154223, size = 100, normalized size = 2.63 \[ A a^{4} x + \frac{B b^{4} x^{6}}{6} + x^{5} \left (\frac{A b^{4}}{5} + \frac{4 B a b^{3}}{5}\right ) + x^{4} \left (A a b^{3} + \frac{3 B a^{2} b^{2}}{2}\right ) + x^{3} \left (2 A a^{2} b^{2} + \frac{4 B a^{3} b}{3}\right ) + x^{2} \left (2 A a^{3} b + \frac{B a^{4}}{2}\right ) \]
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 = 0.29302, size = 131, normalized size = 3.45 \[ \frac{1}{6} \, B b^{4} x^{6} + \frac{4}{5} \, B a b^{3} x^{5} + \frac{1}{5} \, A b^{4} x^{5} + \frac{3}{2} \, B a^{2} b^{2} x^{4} + A a b^{3} x^{4} + \frac{4}{3} \, B a^{3} b x^{3} + 2 \, A a^{2} b^{2} x^{3} + \frac{1}{2} \, B a^{4} x^{2} + 2 \, A a^{3} b x^{2} + A a^{4} x \]
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]