Optimal. Leaf size=59 \[ -\frac{a^3 B}{3 x^3}-\frac{3 a^2 b B}{2 x^2}-\frac{A (a+b x)^4}{4 a x^4}-\frac{3 a b^2 B}{x}+b^3 B \log (x) \]
[Out]
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Rubi [A] time = 0.0683416, antiderivative size = 59, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125 \[ -\frac{a^3 B}{3 x^3}-\frac{3 a^2 b B}{2 x^2}-\frac{A (a+b x)^4}{4 a x^4}-\frac{3 a b^2 B}{x}+b^3 B \log (x) \]
Antiderivative was successfully verified.
[In] Int[((a + b*x)^3*(A + B*x))/x^5,x]
[Out]
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Rubi in Sympy [A] time = 14.4514, size = 56, normalized size = 0.95 \[ - \frac{A \left (a + b x\right )^{4}}{4 a x^{4}} - \frac{B a^{3}}{3 x^{3}} - \frac{3 B a^{2} b}{2 x^{2}} - \frac{3 B a b^{2}}{x} + B b^{3} \log{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**3*(B*x+A)/x**5,x)
[Out]
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Mathematica [A] time = 0.0413322, size = 70, normalized size = 1.19 \[ -\frac{a^3 (3 A+4 B x)+6 a^2 b x (2 A+3 B x)+18 a b^2 x^2 (A+2 B x)+12 A b^3 x^3-12 b^3 B x^4 \log (x)}{12 x^4} \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x)^3*(A + B*x))/x^5,x]
[Out]
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Maple [A] time = 0.01, size = 76, normalized size = 1.3 \[{b}^{3}B\ln \left ( x \right ) -{\frac{3\,a{b}^{2}A}{2\,{x}^{2}}}-{\frac{3\,{a}^{2}bB}{2\,{x}^{2}}}-{\frac{{b}^{3}A}{x}}-3\,{\frac{a{b}^{2}B}{x}}-{\frac{{a}^{2}bA}{{x}^{3}}}-{\frac{{a}^{3}B}{3\,{x}^{3}}}-{\frac{A{a}^{3}}{4\,{x}^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^3*(B*x+A)/x^5,x)
[Out]
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Maxima [A] time = 1.34838, size = 97, normalized size = 1.64 \[ B b^{3} \log \left (x\right ) - \frac{3 \, A a^{3} + 12 \,{\left (3 \, B a b^{2} + A b^{3}\right )} x^{3} + 18 \,{\left (B a^{2} b + A a b^{2}\right )} x^{2} + 4 \,{\left (B a^{3} + 3 \, A a^{2} b\right )} x}{12 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^3/x^5,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.206265, size = 101, normalized size = 1.71 \[ \frac{12 \, B b^{3} x^{4} \log \left (x\right ) - 3 \, A a^{3} - 12 \,{\left (3 \, B a b^{2} + A b^{3}\right )} x^{3} - 18 \,{\left (B a^{2} b + A a b^{2}\right )} x^{2} - 4 \,{\left (B a^{3} + 3 \, A a^{2} b\right )} x}{12 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^3/x^5,x, algorithm="fricas")
[Out]
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Sympy [A] time = 4.63915, size = 75, normalized size = 1.27 \[ B b^{3} \log{\left (x \right )} - \frac{3 A a^{3} + x^{3} \left (12 A b^{3} + 36 B a b^{2}\right ) + x^{2} \left (18 A a b^{2} + 18 B a^{2} b\right ) + x \left (12 A a^{2} b + 4 B a^{3}\right )}{12 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)**3*(B*x+A)/x**5,x)
[Out]
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GIAC/XCAS [A] time = 0.282141, size = 99, normalized size = 1.68 \[ B b^{3}{\rm ln}\left ({\left | x \right |}\right ) - \frac{3 \, A a^{3} + 12 \,{\left (3 \, B a b^{2} + A b^{3}\right )} x^{3} + 18 \,{\left (B a^{2} b + A a b^{2}\right )} x^{2} + 4 \,{\left (B a^{3} + 3 \, A a^{2} b\right )} x}{12 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^3/x^5,x, algorithm="giac")
[Out]