Optimal. Leaf size=64 \[ -\frac{a^3 A}{3 x^3}-\frac{a^2 (a B+3 A b)}{2 x^2}+b^2 \log (x) (3 a B+A b)-\frac{3 a b (a B+A b)}{x}+b^3 B x \]
[Out]
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Rubi [A] time = 0.101765, antiderivative size = 64, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062 \[ -\frac{a^3 A}{3 x^3}-\frac{a^2 (a B+3 A b)}{2 x^2}+b^2 \log (x) (3 a B+A b)-\frac{3 a b (a B+A b)}{x}+b^3 B x \]
Antiderivative was successfully verified.
[In] Int[((a + b*x)^3*(A + B*x))/x^4,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{A a^{3}}{3 x^{3}} - \frac{a^{2} \left (3 A b + B a\right )}{2 x^{2}} - \frac{3 a b \left (A b + B a\right )}{x} + b^{3} \int B\, dx + b^{2} \left (A b + 3 B a\right ) \log{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**3*(B*x+A)/x**4,x)
[Out]
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Mathematica [A] time = 0.060854, size = 67, normalized size = 1.05 \[ b^2 \log (x) (3 a B+A b)-\frac{a^3 (2 A+3 B x)+9 a^2 b x (A+2 B x)+18 a A b^2 x^2-6 b^3 B x^4}{6 x^3} \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x)^3*(A + B*x))/x^4,x]
[Out]
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Maple [A] time = 0.01, size = 72, normalized size = 1.1 \[{b}^{3}Bx+A\ln \left ( x \right ){b}^{3}+3\,B\ln \left ( x \right ) a{b}^{2}-{\frac{3\,{a}^{2}bA}{2\,{x}^{2}}}-{\frac{{a}^{3}B}{2\,{x}^{2}}}-3\,{\frac{a{b}^{2}A}{x}}-3\,{\frac{{a}^{2}bB}{x}}-{\frac{A{a}^{3}}{3\,{x}^{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^3*(B*x+A)/x^4,x)
[Out]
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Maxima [A] time = 1.34797, size = 93, normalized size = 1.45 \[ B b^{3} x +{\left (3 \, B a b^{2} + A b^{3}\right )} \log \left (x\right ) - \frac{2 \, A a^{3} + 18 \,{\left (B a^{2} b + A a b^{2}\right )} x^{2} + 3 \,{\left (B a^{3} + 3 \, A a^{2} b\right )} x}{6 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^3/x^4,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.206592, size = 101, normalized size = 1.58 \[ \frac{6 \, B b^{3} x^{4} + 6 \,{\left (3 \, B a b^{2} + A b^{3}\right )} x^{3} \log \left (x\right ) - 2 \, A a^{3} - 18 \,{\left (B a^{2} b + A a b^{2}\right )} x^{2} - 3 \,{\left (B a^{3} + 3 \, A a^{2} b\right )} x}{6 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^3/x^4,x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.39135, size = 70, normalized size = 1.09 \[ B b^{3} x + b^{2} \left (A b + 3 B a\right ) \log{\left (x \right )} - \frac{2 A a^{3} + x^{2} \left (18 A a b^{2} + 18 B a^{2} b\right ) + x \left (9 A a^{2} b + 3 B a^{3}\right )}{6 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)**3*(B*x+A)/x**4,x)
[Out]
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GIAC/XCAS [A] time = 0.293465, size = 95, normalized size = 1.48 \[ B b^{3} x +{\left (3 \, B a b^{2} + A b^{3}\right )}{\rm ln}\left ({\left | x \right |}\right ) - \frac{2 \, A a^{3} + 18 \,{\left (B a^{2} b + A a b^{2}\right )} x^{2} + 3 \,{\left (B a^{3} + 3 \, A a^{2} b\right )} x}{6 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^3/x^4,x, algorithm="giac")
[Out]