Optimal. Leaf size=44 \[ \frac{(a+b x)^3 (A b-4 a B)}{12 a^2 x^3}-\frac{A (a+b x)^3}{4 a x^4} \]
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Rubi [A] time = 0.0526766, antiderivative size = 44, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125 \[ \frac{(a+b x)^3 (A b-4 a B)}{12 a^2 x^3}-\frac{A (a+b x)^3}{4 a x^4} \]
Antiderivative was successfully verified.
[In] Int[((a + b*x)^2*(A + B*x))/x^5,x]
[Out]
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Rubi in Sympy [A] time = 15.5182, size = 48, normalized size = 1.09 \[ - \frac{A a^{2}}{4 x^{4}} - \frac{B b^{2}}{x} - \frac{a \left (2 A b + B a\right )}{3 x^{3}} - \frac{b \left (A b + 2 B a\right )}{2 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**2*(B*x+A)/x**5,x)
[Out]
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Mathematica [A] time = 0.0249638, size = 47, normalized size = 1.07 \[ -\frac{a^2 (3 A+4 B x)+4 a b x (2 A+3 B x)+6 b^2 x^2 (A+2 B x)}{12 x^4} \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x)^2*(A + B*x))/x^5,x]
[Out]
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Maple [A] time = 0.007, size = 48, normalized size = 1.1 \[ -{\frac{b \left ( Ab+2\,Ba \right ) }{2\,{x}^{2}}}-{\frac{B{b}^{2}}{x}}-{\frac{a \left ( 2\,Ab+Ba \right ) }{3\,{x}^{3}}}-{\frac{A{a}^{2}}{4\,{x}^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^2*(B*x+A)/x^5,x)
[Out]
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Maxima [A] time = 1.33655, size = 69, normalized size = 1.57 \[ -\frac{12 \, B b^{2} x^{3} + 3 \, A a^{2} + 6 \,{\left (2 \, B a b + A b^{2}\right )} x^{2} + 4 \,{\left (B a^{2} + 2 \, A a b\right )} x}{12 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^2/x^5,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.195127, size = 69, normalized size = 1.57 \[ -\frac{12 \, B b^{2} x^{3} + 3 \, A a^{2} + 6 \,{\left (2 \, B a b + A b^{2}\right )} x^{2} + 4 \,{\left (B a^{2} + 2 \, A a b\right )} x}{12 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^2/x^5,x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.34528, size = 54, normalized size = 1.23 \[ - \frac{3 A a^{2} + 12 B b^{2} x^{3} + x^{2} \left (6 A b^{2} + 12 B a b\right ) + x \left (8 A a b + 4 B a^{2}\right )}{12 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)**2*(B*x+A)/x**5,x)
[Out]
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GIAC/XCAS [A] time = 0.305717, size = 69, normalized size = 1.57 \[ -\frac{12 \, B b^{2} x^{3} + 12 \, B a b x^{2} + 6 \, A b^{2} x^{2} + 4 \, B a^{2} x + 8 \, A a b x + 3 \, A a^{2}}{12 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^2/x^5,x, algorithm="giac")
[Out]