Optimal. Leaf size=86 \[ -\frac{a^4 A}{4 x^4}-\frac{a^3 (a B+4 A b)}{3 x^3}-\frac{a^2 b (2 a B+3 A b)}{x^2}+b^3 \log (x) (4 a B+A b)-\frac{2 a b^2 (3 a B+2 A b)}{x}+b^4 B x \]
[Out]
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Rubi [A] time = 0.129126, antiderivative size = 86, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 27, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.074 \[ -\frac{a^4 A}{4 x^4}-\frac{a^3 (a B+4 A b)}{3 x^3}-\frac{a^2 b (2 a B+3 A b)}{x^2}+b^3 \log (x) (4 a B+A b)-\frac{2 a b^2 (3 a B+2 A b)}{x}+b^4 B x \]
Antiderivative was successfully verified.
[In] Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/x^5,x]
[Out]
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Rubi in Sympy [A] time = 35.6051, size = 85, normalized size = 0.99 \[ - \frac{A a^{4}}{4 x^{4}} + B b^{4} x - \frac{a^{3} \left (4 A b + B a\right )}{3 x^{3}} - \frac{a^{2} b \left (3 A b + 2 B a\right )}{x^{2}} - \frac{2 a b^{2} \left (2 A b + 3 B a\right )}{x} + b^{3} \left (A b + 4 B a\right ) \log{\left (x \right )} \]
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**5,x)
[Out]
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Mathematica [A] time = 0.0673062, size = 85, normalized size = 0.99 \[ -\frac{a^4 (3 A+4 B x)}{12 x^4}-\frac{2 a^3 b (2 A+3 B x)}{3 x^3}-\frac{3 a^2 b^2 (A+2 B x)}{x^2}+b^3 \log (x) (4 a B+A b)-\frac{4 a A b^3}{x}+b^4 B x \]
Antiderivative was successfully verified.
[In] Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/x^5,x]
[Out]
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Maple [A] time = 0.012, size = 96, normalized size = 1.1 \[{b}^{4}Bx+A\ln \left ( x \right ){b}^{4}+4\,B\ln \left ( x \right ) a{b}^{3}-{\frac{A{a}^{4}}{4\,{x}^{4}}}-{\frac{4\,A{a}^{3}b}{3\,{x}^{3}}}-{\frac{B{a}^{4}}{3\,{x}^{3}}}-3\,{\frac{A{a}^{2}{b}^{2}}{{x}^{2}}}-2\,{\frac{B{a}^{3}b}{{x}^{2}}}-4\,{\frac{Aa{b}^{3}}{x}}-6\,{\frac{B{a}^{2}{b}^{2}}{x}} \]
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^5,x)
[Out]
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Maxima [A] time = 0.677936, size = 128, normalized size = 1.49 \[ B b^{4} x +{\left (4 \, B a b^{3} + A b^{4}\right )} \log \left (x\right ) - \frac{3 \, A a^{4} + 24 \,{\left (3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right )} x^{3} + 12 \,{\left (2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right )} x^{2} + 4 \,{\left (B a^{4} + 4 \, A a^{3} b\right )} x}{12 \, x^{4}} \]
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^5,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.281783, size = 136, normalized size = 1.58 \[ \frac{12 \, B b^{4} x^{5} + 12 \,{\left (4 \, B a b^{3} + A b^{4}\right )} x^{4} \log \left (x\right ) - 3 \, A a^{4} - 24 \,{\left (3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right )} x^{3} - 12 \,{\left (2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right )} x^{2} - 4 \,{\left (B a^{4} + 4 \, A a^{3} b\right )} x}{12 \, x^{4}} \]
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^5,x, algorithm="fricas")
[Out]
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Sympy [A] time = 5.29851, size = 94, normalized size = 1.09 \[ B b^{4} x + b^{3} \left (A b + 4 B a\right ) \log{\left (x \right )} - \frac{3 A a^{4} + x^{3} \left (48 A a b^{3} + 72 B a^{2} b^{2}\right ) + x^{2} \left (36 A a^{2} b^{2} + 24 B a^{3} b\right ) + x \left (16 A a^{3} b + 4 B a^{4}\right )}{12 x^{4}} \]
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**5,x)
[Out]
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GIAC/XCAS [A] time = 0.269471, size = 130, normalized size = 1.51 \[ B b^{4} x +{\left (4 \, B a b^{3} + A b^{4}\right )}{\rm ln}\left ({\left | x \right |}\right ) - \frac{3 \, A a^{4} + 24 \,{\left (3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right )} x^{3} + 12 \,{\left (2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right )} x^{2} + 4 \,{\left (B a^{4} + 4 \, A a^{3} b\right )} x}{12 \, x^{4}} \]
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^5,x, algorithm="giac")
[Out]