Optimal. Leaf size=71 \[ \frac{A b^2 x^{m+3}}{m+3}+\frac{b x^{m+4} (2 A c+b B)}{m+4}+\frac{c x^{m+5} (A c+2 b B)}{m+5}+\frac{B c^2 x^{m+6}}{m+6} \]
[Out]
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Rubi [A] time = 0.118895, antiderivative size = 71, 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 \[ \frac{A b^2 x^{m+3}}{m+3}+\frac{b x^{m+4} (2 A c+b B)}{m+4}+\frac{c x^{m+5} (A c+2 b B)}{m+5}+\frac{B c^2 x^{m+6}}{m+6} \]
Antiderivative was successfully verified.
[In] Int[x^m*(A + B*x)*(b*x + c*x^2)^2,x]
[Out]
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Rubi in Sympy [A] time = 15.2409, size = 63, normalized size = 0.89 \[ \frac{A b^{2} x^{m + 3}}{m + 3} + \frac{B c^{2} x^{m + 6}}{m + 6} + \frac{b x^{m + 4} \left (2 A c + B b\right )}{m + 4} + \frac{c x^{m + 5} \left (A c + 2 B b\right )}{m + 5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**m*(B*x+A)*(c*x**2+b*x)**2,x)
[Out]
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Mathematica [A] time = 0.0835703, size = 64, normalized size = 0.9 \[ x^{m+3} \left (\frac{A b^2}{m+3}+\frac{c x^2 (A c+2 b B)}{m+5}+\frac{b x (2 A c+b B)}{m+4}+\frac{B c^2 x^3}{m+6}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x^m*(A + B*x)*(b*x + c*x^2)^2,x]
[Out]
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Maple [B] time = 0.007, size = 246, normalized size = 3.5 \[{\frac{{x}^{3+m} \left ( B{c}^{2}{m}^{3}{x}^{3}+A{c}^{2}{m}^{3}{x}^{2}+2\,Bbc{m}^{3}{x}^{2}+12\,B{c}^{2}{m}^{2}{x}^{3}+2\,Abc{m}^{3}x+13\,A{c}^{2}{m}^{2}{x}^{2}+B{b}^{2}{m}^{3}x+26\,Bbc{m}^{2}{x}^{2}+47\,B{c}^{2}m{x}^{3}+A{b}^{2}{m}^{3}+28\,Abc{m}^{2}x+54\,A{c}^{2}m{x}^{2}+14\,B{b}^{2}{m}^{2}x+108\,Bbcm{x}^{2}+60\,B{c}^{2}{x}^{3}+15\,A{b}^{2}{m}^{2}+126\,Abcmx+72\,A{c}^{2}{x}^{2}+63\,B{b}^{2}mx+144\,Bbc{x}^{2}+74\,A{b}^{2}m+180\,Abcx+90\,{b}^{2}Bx+120\,{b}^{2}A \right ) }{ \left ( 6+m \right ) \left ( 5+m \right ) \left ( 4+m \right ) \left ( 3+m \right ) }} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^m*(B*x+A)*(c*x^2+b*x)^2,x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^2*(B*x + A)*x^m,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.284639, size = 293, normalized size = 4.13 \[ \frac{{\left ({\left (B c^{2} m^{3} + 12 \, B c^{2} m^{2} + 47 \, B c^{2} m + 60 \, B c^{2}\right )} x^{6} +{\left ({\left (2 \, B b c + A c^{2}\right )} m^{3} + 144 \, B b c + 72 \, A c^{2} + 13 \,{\left (2 \, B b c + A c^{2}\right )} m^{2} + 54 \,{\left (2 \, B b c + A c^{2}\right )} m\right )} x^{5} +{\left ({\left (B b^{2} + 2 \, A b c\right )} m^{3} + 90 \, B b^{2} + 180 \, A b c + 14 \,{\left (B b^{2} + 2 \, A b c\right )} m^{2} + 63 \,{\left (B b^{2} + 2 \, A b c\right )} m\right )} x^{4} +{\left (A b^{2} m^{3} + 15 \, A b^{2} m^{2} + 74 \, A b^{2} m + 120 \, A b^{2}\right )} x^{3}\right )} x^{m}}{m^{4} + 18 \, m^{3} + 119 \, m^{2} + 342 \, m + 360} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^2*(B*x + A)*x^m,x, algorithm="fricas")
[Out]
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Sympy [A] time = 4.45017, size = 1027, normalized size = 14.46 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**m*(B*x+A)*(c*x**2+b*x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.275712, size = 524, normalized size = 7.38 \[ \frac{B c^{2} m^{3} x^{6} e^{\left (m{\rm ln}\left (x\right )\right )} + 2 \, B b c m^{3} x^{5} e^{\left (m{\rm ln}\left (x\right )\right )} + A c^{2} m^{3} x^{5} e^{\left (m{\rm ln}\left (x\right )\right )} + 12 \, B c^{2} m^{2} x^{6} e^{\left (m{\rm ln}\left (x\right )\right )} + B b^{2} m^{3} x^{4} e^{\left (m{\rm ln}\left (x\right )\right )} + 2 \, A b c m^{3} x^{4} e^{\left (m{\rm ln}\left (x\right )\right )} + 26 \, B b c m^{2} x^{5} e^{\left (m{\rm ln}\left (x\right )\right )} + 13 \, A c^{2} m^{2} x^{5} e^{\left (m{\rm ln}\left (x\right )\right )} + 47 \, B c^{2} m x^{6} e^{\left (m{\rm ln}\left (x\right )\right )} + A b^{2} m^{3} x^{3} e^{\left (m{\rm ln}\left (x\right )\right )} + 14 \, B b^{2} m^{2} x^{4} e^{\left (m{\rm ln}\left (x\right )\right )} + 28 \, A b c m^{2} x^{4} e^{\left (m{\rm ln}\left (x\right )\right )} + 108 \, B b c m x^{5} e^{\left (m{\rm ln}\left (x\right )\right )} + 54 \, A c^{2} m x^{5} e^{\left (m{\rm ln}\left (x\right )\right )} + 60 \, B c^{2} x^{6} e^{\left (m{\rm ln}\left (x\right )\right )} + 15 \, A b^{2} m^{2} x^{3} e^{\left (m{\rm ln}\left (x\right )\right )} + 63 \, B b^{2} m x^{4} e^{\left (m{\rm ln}\left (x\right )\right )} + 126 \, A b c m x^{4} e^{\left (m{\rm ln}\left (x\right )\right )} + 144 \, B b c x^{5} e^{\left (m{\rm ln}\left (x\right )\right )} + 72 \, A c^{2} x^{5} e^{\left (m{\rm ln}\left (x\right )\right )} + 74 \, A b^{2} m x^{3} e^{\left (m{\rm ln}\left (x\right )\right )} + 90 \, B b^{2} x^{4} e^{\left (m{\rm ln}\left (x\right )\right )} + 180 \, A b c x^{4} e^{\left (m{\rm ln}\left (x\right )\right )} + 120 \, A b^{2} x^{3} e^{\left (m{\rm ln}\left (x\right )\right )}}{m^{4} + 18 \, m^{3} + 119 \, m^{2} + 342 \, m + 360} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^2*(B*x + A)*x^m,x, algorithm="giac")
[Out]