Optimal. Leaf size=38 \[ \frac{B (b+c x)^5}{5 c^2}-\frac{(b+c x)^4 (b B-A c)}{4 c^2} \]
[Out]
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Rubi [A] time = 0.0645025, antiderivative size = 38, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1 \[ \frac{B (b+c x)^5}{5 c^2}-\frac{(b+c x)^4 (b B-A c)}{4 c^2} \]
Antiderivative was successfully verified.
[In] Int[((A + B*x)*(b*x + c*x^2)^3)/x^3,x]
[Out]
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Rubi in Sympy [A] time = 12.5584, size = 31, normalized size = 0.82 \[ \frac{B \left (b + c x\right )^{5}}{5 c^{2}} + \frac{\left (b + c x\right )^{4} \left (A c - B b\right )}{4 c^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((B*x+A)*(c*x**2+b*x)**3/x**3,x)
[Out]
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Mathematica [A] time = 0.0188771, size = 67, normalized size = 1.76 \[ A b^3 x+\frac{1}{2} b^2 x^2 (3 A c+b B)+\frac{1}{4} c^2 x^4 (A c+3 b B)+b c x^3 (A c+b B)+\frac{1}{5} B c^3 x^5 \]
Antiderivative was successfully verified.
[In] Integrate[((A + B*x)*(b*x + c*x^2)^3)/x^3,x]
[Out]
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Maple [B] time = 0.002, size = 73, normalized size = 1.9 \[{\frac{B{c}^{3}{x}^{5}}{5}}+{\frac{ \left ( A{c}^{3}+3\,Bb{c}^{2} \right ){x}^{4}}{4}}+{\frac{ \left ( 3\,Ab{c}^{2}+3\,B{b}^{2}c \right ){x}^{3}}{3}}+{\frac{ \left ( 3\,A{b}^{2}c+B{b}^{3} \right ){x}^{2}}{2}}+A{b}^{3}x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((B*x+A)*(c*x^2+b*x)^3/x^3,x)
[Out]
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Maxima [A] time = 0.69716, size = 93, normalized size = 2.45 \[ \frac{1}{5} \, B c^{3} x^{5} + A b^{3} x + \frac{1}{4} \,{\left (3 \, B b c^{2} + A c^{3}\right )} x^{4} +{\left (B b^{2} c + A b c^{2}\right )} x^{3} + \frac{1}{2} \,{\left (B b^{3} + 3 \, A b^{2} c\right )} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^3*(B*x + A)/x^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.258408, size = 93, normalized size = 2.45 \[ \frac{1}{5} \, B c^{3} x^{5} + A b^{3} x + \frac{1}{4} \,{\left (3 \, B b c^{2} + A c^{3}\right )} x^{4} +{\left (B b^{2} c + A b c^{2}\right )} x^{3} + \frac{1}{2} \,{\left (B b^{3} + 3 \, A b^{2} c\right )} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^3*(B*x + A)/x^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.148727, size = 73, normalized size = 1.92 \[ A b^{3} x + \frac{B c^{3} x^{5}}{5} + x^{4} \left (\frac{A c^{3}}{4} + \frac{3 B b c^{2}}{4}\right ) + x^{3} \left (A b c^{2} + B b^{2} c\right ) + x^{2} \left (\frac{3 A b^{2} c}{2} + \frac{B b^{3}}{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x+A)*(c*x**2+b*x)**3/x**3,x)
[Out]
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GIAC/XCAS [A] time = 0.266424, size = 97, normalized size = 2.55 \[ \frac{1}{5} \, B c^{3} x^{5} + \frac{3}{4} \, B b c^{2} x^{4} + \frac{1}{4} \, A c^{3} x^{4} + B b^{2} c x^{3} + A b c^{2} x^{3} + \frac{1}{2} \, B b^{3} x^{2} + \frac{3}{2} \, A b^{2} c x^{2} + A b^{3} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^3*(B*x + A)/x^3,x, algorithm="giac")
[Out]