Optimal. Leaf size=49 \[ -\frac{a^2 A}{3 x^3}-\frac{a (a B+2 A b)}{2 x^2}-\frac{b (2 a B+A b)}{x}+b^2 B \log (x) \]
[Out]
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Rubi [A] time = 0.065297, antiderivative size = 49, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 25, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.08 \[ -\frac{a^2 A}{3 x^3}-\frac{a (a B+2 A b)}{2 x^2}-\frac{b (2 a B+A b)}{x}+b^2 B \log (x) \]
Antiderivative was successfully verified.
[In] Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/x^4,x]
[Out]
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Rubi in Sympy [A] time = 20.7335, size = 44, normalized size = 0.9 \[ - \frac{A a^{2}}{3 x^{3}} + B b^{2} \log{\left (x \right )} - \frac{a \left (2 A b + B a\right )}{2 x^{2}} - \frac{b \left (A b + 2 B a\right )}{x} \]
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)/x**4,x)
[Out]
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Mathematica [A] time = 0.0465665, size = 48, normalized size = 0.98 \[ b^2 B \log (x)-\frac{a^2 (2 A+3 B x)+6 a b x (A+2 B x)+6 A b^2 x^2}{6 x^3} \]
Antiderivative was successfully verified.
[In] Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/x^4,x]
[Out]
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Maple [A] time = 0.009, size = 52, normalized size = 1.1 \[{b}^{2}B\ln \left ( x \right ) -{\frac{A{a}^{2}}{3\,{x}^{3}}}-{\frac{abA}{{x}^{2}}}-{\frac{{a}^{2}B}{2\,{x}^{2}}}-{\frac{{b}^{2}A}{x}}-2\,{\frac{abB}{x}} \]
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)/x^4,x)
[Out]
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Maxima [A] time = 0.679547, size = 68, normalized size = 1.39 \[ B b^{2} \log \left (x\right ) - \frac{2 \, A a^{2} + 6 \,{\left (2 \, B a b + A b^{2}\right )} x^{2} + 3 \,{\left (B a^{2} + 2 \, A a b\right )} x}{6 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^2 + 2*a*b*x + a^2)*(B*x + A)/x^4,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.270435, size = 72, normalized size = 1.47 \[ \frac{6 \, B b^{2} x^{3} \log \left (x\right ) - 2 \, A a^{2} - 6 \,{\left (2 \, B a b + A b^{2}\right )} x^{2} - 3 \,{\left (B a^{2} + 2 \, A a b\right )} x}{6 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^2 + 2*a*b*x + a^2)*(B*x + A)/x^4,x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.67538, size = 51, normalized size = 1.04 \[ B b^{2} \log{\left (x \right )} - \frac{2 A a^{2} + x^{2} \left (6 A b^{2} + 12 B a b\right ) + x \left (6 A a b + 3 B a^{2}\right )}{6 x^{3}} \]
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)/x**4,x)
[Out]
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GIAC/XCAS [A] time = 0.268908, size = 69, normalized size = 1.41 \[ B b^{2}{\rm ln}\left ({\left | x \right |}\right ) - \frac{2 \, A a^{2} + 6 \,{\left (2 \, B a b + A b^{2}\right )} x^{2} + 3 \,{\left (B a^{2} + 2 \, A a b\right )} x}{6 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^2 + 2*a*b*x + a^2)*(B*x + A)/x^4,x, algorithm="giac")
[Out]